International Congress in Honour of Professor Ravi P. Agarwal

International Congress in Honour of

Professor Ravi P. Agarwal

June 23–26, 2014

Uludag University, Bursa–Turkey

2 International Congress in Honour of Professor Ravi P. Agarwal

Scientific Committee

R. P. Agarwal (USA) [email protected]. L. Bona (USA) [email protected]. Bruno (Russia) [email protected]. N. Cangul (Turkey) [email protected]. S. Cevik (Turkey) [email protected]. Di Benedetto (USA) [email protected]. Finn (USA) [email protected]. P. Gilbert (USA) [email protected]. M. Haddad (USA) [email protected]. Kiguradze (Georgia) [email protected]. A. Kirk (USA) [email protected]. Lasiecka (USA) [email protected]. Lokesha (India) [email protected] To-Ming Lau (Canada) [email protected]. Mawhin (Belgium) [email protected]. Milovanovic (Serbia) [email protected]. Mordukhovich (USA) [email protected]. Neuberger (USA) [email protected]. Nieto (Spain) [email protected]. Motreanu (France) [email protected]. O’ Regan (Ireland) [email protected]. Park (Korea) [email protected]. Peterson (USA) [email protected]. Radulescu (Romania) [email protected]. Reich (Israel) [email protected]. Savas (Turkey) [email protected]. D. Schechter (USA) [email protected]. Simsek (Turkey) [email protected]. Takahashi (Japan) [email protected]. Tascı (Turkey) [email protected]. Triggiani (USA) [email protected]. R. L. Webb (UK) [email protected]. Xu (Taiwan) [email protected]

International Congress in Honour of Professor Ravi P. Agarwal 3

Local Organizing Committee

Ismail Naci Cangul (Uludag University, Turkey)Ahmet Sinan Cevik (Selcuk University, Turkey)Nihat Akgunes (Selcuk University, Turkey)Elvan Akın (Missouri University, USA)Firat Ates (Balikesir University, Turkey)Muge Capkin (Uludag University, Turkey)Elif Cetin (Uludag University, Turkey)Musa Demirci (Uludag University, Turkey)Ayse Feza Guvenilir (Ankara University, Turkey)Sebahattin Ikikardes (Balikesir University, Turkey)Nazlı Yildiz Ikikardes (Balikesir University, Turkey)Ilker Inam (Uludag University, Turkey)Erdal Karapınar (Atlm University, Turkey)Billur Kaymakcalan (Cankaya University, Turkey)Hacer Ozden (Uludag University, Turkey)Birsen Ozgur (Uludag University, Turkey)Metin Ozturk (Uludag University, Turkey)Recep Sahin (Balikesir University, Turkey)Umit Sarp (Balikesir University, Turkey)Ekrem Savas (Istanbul Commerce University, Turkey)Gokhan Soydan (Uludag University, Turkey)Kenan Tas (Cankaya University, Turkey)Dursun Tascı (Gazi University, Turkey)Ahmet Tekcan (Uludag University, Turkey)Sibel Yalcin Tokgoz (Uludag University, Turkey)Elif Yasar (Uludag University, Turkey)Emrullah Yasar (Uludag University, Turkey)Aysun Yurttas (Uludag University, Turkey)


Preface

On behalf of the Scientific and Organising Committees, I would like to welcome you all to Bursa forthis International Congress.

First of all, I would like to mention the willingness and capacity of the Mathematics Department atUludag University to organize and actively take part in Mathematical events. We have been organizingnumerous national and international congresses, conferences, workshops and seminars with the help ofour colleagues at other universities. The following are just a few examples of the events in last years.

On 21st-23rd August, 2008, we organized The Twentieth International Congress of the Jang-jeon Mathematical Society, of which I have been honoured to be a member, in Karinna Hotel atMount Uludag. The refereed proceedings of this congress were published in Advanced Studies inContemporary Mathematics and Proceedings of the Jangjeon Mathematical Society.

Following this event, we organized The International Congress in Honour of Professor H. M.Srivastava on his 70th Birth Anniversary, again in Karinna Hotel on 18th-21st August, 2010. Theduly-refereed prooceedings of this congress were published as a special volume of the Elsevier journalApplied Mathematics and Computation.

2011 was the year that we hosted the 24th National Mathematics Symposium at Uludag Uni-versity.

Finally The International Congress in Honour of Professor Hari M. Srivastava was heldat the Auditorium at the Campus of Uludag University, Bursa, Turkey on 23rd-26th August, 2012. Theduly-refereed prooceedings of this congress were published in special volumes of the four open accessSpringer journals Advances in Difference Equations, Boundary Value Problems, Fixed PointTheory and Applications and Journal of Inequalities and Applications.

Prof. Dr. Ravi P. Agarwal has been coworking with many Turkish mathematicians in a wide rangeof topics and his contributions, in particular to Turkish mathematics and mathematicians, are endless.This is one of the reasons that made me proud to organize The International Congress in Honourof Professor Ravi P. Agarwal on 23rd-26th June, 2014. We hoped to thank him, at least partially, forhis support and contributions to Turkish mathematicians. It is my great pleasure to welcome you all toThe International Congress in Honour of Professor Ravi P. Agarwal and to Bursa.

The duly refereed proceedings of this congress will be published in two special issues in open accessSpringer journals Advances in Difference Equations and Applications and Journal of Inequal-ities and Applications. I especially thank in advance to the editor Prof. Dr. Ravi P. Agarwal,and to the guest editors Prof. Dr. Billur Kaymakcalan, Prof. Dr. Elvan Akın and Prof. Dr.Erdal Karapınar who spend a lot of time and effort with me to produce the best possible special issuesto be remembered for many years.

Please allow me to thank all my colleagues and students who worked with me for months to makethis congress a success. One particular mathematician needs to be mentioned especially: My good friendand coworker Prof. Dr. Ahmet Sinan Cevik, who is the co-chair of this congress and helped me inmany aspects. I am proud to organize all these meetings together with this special people and I wish ourcowork and friendship will go on forever. My final thanks go to Prof. Dr. Ahmet Tekcan who hadspent serious amount of time to produce this booklet as nicely as it is.

Finally, on behalf of all the friends and colleagues, I take this opportunity to wish Prof. Dr. Agarwala happy life together with all his beloved ones and continuation of his contributions to Mathematics andMathematicians.

Prof. Dr. Ismail Naci CangulChair of the Congress,Dean of the Faculty of Arts and ScienceUludag University, Gorukle Campus, 16059 Bursa, [email protected], [email protected]://cangul.home.uludag.edu.tr/http://www.ismailnacicangul.com/


About Prof. Dr. Ravi P. Agarwal

Age and Date of Birth: 66 years, 10th July, 1947Present Position: Professor & Chairman, Department of Mathematics Texas A&M University-

Kingsville Kingsville, TX 78363, U.S.A.e-mail: [email protected]

Telephone Numbers: 1(361)593 - 2600(office) 1(361)221 - 1388(personal)Degrees: Master in Science (1969) Agra Univ., 1st class, 2nd position Ph.D. (1973) Indian Institute

of Technology, Madras, IndiaField of Research: Numerical Analysis, Differential and Difference Equations, Inequalities, Fixed

Point TheoremsResearch Experience: 44 years

Research Publications: Over 1175 research papers in the following Journals and Series:

1. Acta Applicandae Mathematicae2. Acta Mathematica Hungarica3. Advances in Difference Equations4. Advances in Mathematical Sciences and Application5. Aequationes Mathematicae6. Analele Stiintifice ale Universitatii. ‘Al. I. Cuza’ din Iasi7. Annales Polonici Mathematici8. Applied Mathematics and Computation9. Applied Mathematics Letters10. Applicable Analysis11. Archivum Mathematicum (Brno)12. Atti della Accad. Nazionale Dei Lincei13. BIT14. Boundary Value Problems15. Bulletin of the Institute of Mathematics, Academia Sinica16. Bulletin UMI17. Chinese Journal of Mathematics18. Communications in Applied Analysis19. Communications in Applied Numerical Methods20. Computers and Mathematics with Applications21. Differential and Integral Equations22. Dynamic Systems and Applications23. *Dynamic Systems and Applications, Dynamic Publishers24. Dynamics of Continuous, Discrete and Impulsive Systems25. Fixed Point Theory and Applications26. Fluid Dynamics Research27. Functional Differential Equations28. Funkcialaj Ekvacioj29. Georgian Mathematical Journal30. Hiroshima Mathematical Journal31. IMA Journal of Applied Mathematics32. Indian Journal of Pure and Applied Mathematics33. International Journal of Computer Mathematics34. *International Series of Numerical Mathematics, Birkhauser35. Japan Journal of Industrial and Applied Mathematics36. Journal of Applied Mathematics and Stochastic Analysis


37. Journal of Approximation Theory38. Journal of the Australian Mathematical Society. Series A39. Journal of the Australian Mathematical Society. Series B40. Journal of Computational and Applied Mathematics41. Journal of Difference Equations and Applications42. Journal of Differential Equations43. Journal of Inequalities and Applications44. Journal of the Korean Mathematical Society45. Journal of the London Mathematical Society46. Journal of Mathematical Analysis and Applications47. Journal of Mathematical and Physical Sciences48. Journal of Nonlinear and Convex Analysis49. Journal of Optimization Theory and Applications50. Korean Journal of Computational and Applied Mathematics51. *Lecture Notes in Mathematics, Springer-Verlag52. Mathematica Slovaca53. Mathematical Inequalities and Applications54. Mathematical Methods in the Applied Sciences55. Mathematical and Computer Modelling56. Mathematical Problems in Engineering: Theory, Methods and Applications57. Mathematics Seminar Notes, Kobe University58. Mathematika59. Mathematische Nachrichten60. *Matscience Reports61. Neural, Parallel and Scientific Computations62. Nonlinear Analysis Forum63. Nonlinear Analysis : Theory, Methods and Applications64. Nonlinear Functional Analysis and Applications65. Nonlinear World66. *North-Holland Mathematics Studies67. PanAmerican Mathematical Journal68. Proceedings of the American Mathematical Society69. *Proceedings of the Conference of ISTAM70. *Proceedings of the International Conference on Difference Equations and Applications, Gordon

and Breach71. *Proceedings of the First World Congress of Nonlinear Analysts, Walter de Gruyter72. Proceedings of the Indian Academy of Sciences73. Proceedings of the Royal Society of Edinburgh74. Proceedings of the Edinburgh Mathematical Society75. *Proceedings of Symposia in Applied Mathematics, American Math. Soc.76. Proceedings of the Tamil Nadu Acad. Sci.77. Publications of the Research Institute for Mathematical Sciences78. Results in Mathematics79. Rivista di Math. della Univ. Parma80. Rocky Mountain Journal of Mathematics81. Series in Mathematical Analysis and Applications, Gordon and Breach82. *Stability and Control: Theory, Methods and Applications, Gordon and Breach83. Studies in Applied Mathematics84. Tamkang Journal of Mathematics85. Tohuku Mathematical Journal86. Topological Methods in Nonlinear Analysis87. Utilitas Mathematica


88. ZAA89. ZAMM(* Conference Proceedings/ Special Volumes)

Monographs and Books:

(1) R.P. Agarwal, Boundary Value Problems for Higher Order Differential Equations, World Scientific,Singapore, Philadelphia, 1986, p. 307.

‘This comprehensive monograph provides an exhaustive state of the art coverage of basic results onboundary value problems associated with higher–order differential equations. It is without question oneof the most through reviews I have seen, on any subject. Those doing research in this field would be welladvised to refer to this work. The author consistently poses questions to researchers who are looking foropen problems.’ (Mathematical Reviews)

‘The monograph is an excellent account of the various techniques available in the literature to proveexistence and uniqueness of various boundary value problems which occur in applications. Graduatestudents and research mathematicians will find it very useful.’ (Zentralblatt fur Mathematik)

(2) R.P. Agarwal and R.C. Gupta, Essentials of Ordinary Differential Equations, McGraw-Hill BookCo., Singapore, New York, 1991, p.467.

(3) R.P. Agarwal, Difference Equations and Inequalities : Theory, Methods and Applications, MarcelDekker, Inc., New York, 1992, p.777.

‘This book is a virtual encyclopedia of results concerning difference equations. It is well written andis easy to read. This book covers over 400 recent publications. This book should not only be of interestto mathematicians and statisticians but also to electrical engineers, biologists, economists, psychologists,and sociologists to name a few. This indeed is a very good book to have in ones own personal library.’(Mathematical Reviews)

‘This new monograph combines all aspects of the theory and methods of solutions of difference equa-tions and their applications in real world problems providing in–depth coverage of more than 400 recentpublications. This monograph with the wealth of information it contains is very well come.’(Newsletteron Computational and Applied Mathematics)

‘This book contains a complete account of standard results concerning difference equations, as well asan extensive discussion of recent papers concerning the theory and practice of their solutions. This bookshould be useful both as textbook and for reference.’(Mathematika)

‘This book is essential for the enrichment of knowledge in mathematics, physics and statistics. Thecomprehensive compilation of the book is useful for researchers of natural philosophy.’ (Indian J. Physics)

‘Comprehensive treatment develops discrete versions of Rolle’s, mean value, Kneser’s theorems · · · ’(TheAmerican Mathematical Monthly)

‘This excellent monograph combines all aspects of the theory and methods of solutions of differenceequations and their applications providing in–depth coverage of more than 400 recent publications. Itserves as a basic reference for mathematicians and users of mathematics interested in differential anddifference equations and their applications.’(Acta Sci. Math. Szeged)

‘It is a definite reference for applied mathematicians, numerical analysts, physicists, engineers, andgraduate–level students in courses on difference equations.’(INSPEC The Institute of Electrical Engineers)

‘Focusing on a wide range of possible mathematical uses, the book offers various methods of solvinglinear and nonlinear difference equations.’(Bulletin Bibliographique)

‘Deals with the many aspects of difference equations including theory, methods of solutions, andapplications. Reviews more than 400 recent related publications.’ (The New York Public Library)

(4) R.P. Agarwal and V. Lakshmikantham, Uniqueness and Nonuniqueness Criteria for OrdinaryDifferential Equations, World Scientific, Singapore, 1993, p. 312.

‘The book is devoted to a branch of the theory of differential equations that is classical on the onehand but still alive and developing on the other hand. The book is very interesting and well written.It is warmly recommended to any student in analysis and to any specialist in the theory of differentialequations.’ (Mathematical Reviews and Zentralblatt fur Mathematik)


(5) R.P. Agarwal and P.J.Y. Wong, Error Inequalities in Polynomial Interpolation and Their Appli-cations, Kluwer Academic Publishers, Dordrecht, 1993, p.365.

‘A main theme of this book lies behind the selection and organization of the material in it is theuse of interpolation in the theory of ordinary differential equations · · · . It will no doubt find uses amongspecialists in differential equations. Otherwise, the wealth of detail and the precision of the error estimatesin it go beyond what is generally available in book or monograph form and commend the work to a moregeneral audience.’ (Journal of Approximation Theory)

(6) R.P. Agarwal and R.C. Gupta, Solutions Manual to Accompany Essentials of Ordinary DifferentialEquations, McGraw-Hill Book Co., Singapore, New York, 1993, p.209.

(7) R.P. Agarwal and P.Y.H. Pang, Opial Inequalities with Applications in Differential and DifferenceEquations, Kluwer Academic Publishers, Dordrecht, 1995, p.393.

‘The monograph under review presents a complete survey of results related to the Opial’s inequalitydeveloped over the last three decades · · · . The book under review is very well written and most of thematerial is presented with detailed proofs. The book can be warmly recommended not only to specialistworking in the area of mathematical analysis and applications but also to graduate students, engineersand researchers in the applied sciences.’ (Zentralblatt fur Mathematik)

(8) R.P. Agarwal and P.J.Y. Wong, Advanced Topics in Difference Equations, Kluwer AcademicPublishers, Dordrecht, 1997, p.507.

‘One of the specialists in the field is without doubt Ravi P Agarwal. His previous book DifferenceEquations and Inequalities (1992) is a survey of the theory of difference equations and contains a wealthof information for the researchers. This new book, co–authored by Patricia J. Y. Wong, can be seen asan update of the first one · · · . The results in this book are of great interest to other specialists in thefield. This book offer an easy way to get access to them.’ (Mathematical Reviews)

‘The book contains a collection of recent results and it will serve as a reference book for researchers indiscrete dynamical systems and their applications and reader will also find material, which is not availablein other books on difference equations. It will also be of interest to graduate students interested in thetheory of finite difference equations and their applications. The presentation is clear and it is a welcomeaddition to the literature.’ (Zentralblatt fur Mathematik)

(9) R.P. Agarwal, Focal Boundary Value Problems for Differential and Difference Equations, KluwerAcademic Publishers, Dordrecht, 1998, p.289.

‘Agarwal’s great knowledge of the literature in this area makes this book very appealing. The book willbe useful for a graduate course concerned with boundary value problems for either differential equationsor difference equations. It also would be an excellent book for mathematicians doing research in thisarea.’ (Mathematical Reviews)

(10) R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Positive Solutions of Differential, Difference andIntegral Equations, Kluwer Academic Publishers, Dordrecht, 1999, p.417.

‘The majority of the book is devoted to some of the recent developments by the authors. The bookshould be a good reference book and the extensive bibliography could prove to be very helpful. In addition,the examples at the end of each chapter are a good source of illustrative material.’ (Mathematical Reviews)

(11) R.P. Agarwal, Difference Equations and Inequalities: Second Edition, Revised and Expended,Marcel Dekker, New York, 2000, xv+980pp.

(12) R.P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, CambridgeUniversity Press, Cambridge, 2001, 170pp.

(13) R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Difference and FunctionalDifferential Equations, Kluwer Academic Publishers, Dordrecht, 2000, 337pp.

‘This good monograph contains some of the recent developments in the oscillation theory of differenceand functional-differential equations (FDEs)· · · . It provides an excellent reference to the recent work forresearch workers in this interesting field.’ (Mathematical Reviews)

(14) R.P. Agarwal and D. O’Regan, Infinite Interval Problems for Differential, Difference and IntegralEquations, Kluwer Academic Publishers, Dordrecht, 2001, 341pp.

‘This book develops the basic ideas used in proving the existence of solutions to boundary valueproblems on infinite intervals and it mainly contains the results which the authors have obtained in their


research during the last decade.’ Mathematical Reviews)

(15) R.P. Agarwal, M. Meehan and D. O’Regan, Nonlinear Integral Equations and Inclusions, NovaScience Publishers, New York, 2001, 362pp.

(16) R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Second Order Linear, Half–linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, The Netherlands,2002, 672pp.

‘Those who are already in the field will welcome the systematic organization of the material and findthe book to be a valuable reference.’(Mathematical Reviews)

(17) R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Second Order Dynamic Equa-tions, Taylor & Francis, U.K., 2003, 404pp.

‘The authors study systematically various techniques about oscillation and nonoscillation of each typeof equations. There are numerous examples in each chapter and each chapter ends with detailed historicalnotes and an extensive list of references. The book is very readable and it is a valuable source and animportant contribution to oscillation theory.’(Mathematical Reviews)

(18) R.P. Agarwal and D. O’Regan, Singular Differential and Integral Equations with Applications,Kluwer Academic Publishers, Dordrecht, 2003, 402pp.

‘The authors have produced a monograph in which they present some of the recent developmentin existence of solutions theory of nonlinear singular integral and differential equations. In addition totheory, the monograph focuses on applications. Much of the material focuses on recent developments ofthe authors. A primary purpose of the monograph is to provide a readable account and introduce thematerial to a broader audience.’ (Mathematical Reviews)

(19) R.P. Agarwal, M. Bohner and W.-T. Li, Nonoscillation and Oscillation Theory for FunctionalDifferential Equations, Marcel Dekker, New York, 2004, 376pp.

(20) R.P. Agarwal, M. Bohner, S.R. Grace and D. O’Regan, Discrete Oscillation Theory, HindawiPublishing Corporation, 2005, 1000pp.

‘This is truly a compendium of many different results, all having a relation in some way to resultswhich may or may not be fairly well known for the continuous case. One of the very useful featuresof this book is the discussion at the end of each chapter of the results presented and references to theoriginal sources, as far as the authors are aware. Moreover, the authors have included a large number ofexamples throughout which serve to illustrate the many and varied results which are obtained. All of theauthors are very well known in oscillation theory and have all contributed a great deal to this area. It isindeed a useful addition to the literature to have such a comprehensive survey of the area and to pointthe direction to new results. It will serve as a valuable reference in the area for many years to come.’(Mathematical Reviews)

(21) R.P. Agarwal and D. O’Regan, An Introduction to Ordinary Differential Equations, Springer,New York, 2008.

(22) R.P. Agarwal and D. O’Regan, Ordinary and Partial Differential Equations with Special Func-tions, Fourier Series and Boundary Value Problems, Springer, New York, 2009.

(23) R.P. Agarwal, D. O’Regan and D.R. Sahu, Fixed Point Theory for Lipschitzian–type Mappingswith Applications, Springer, New York, 2009

(24) R.P. Agarwal, S. Ding and C.A. Nolder, Inequalities for Differential Forms, Springer, New York,2009.

(25) K. Perera, R.P. Agarwal and D. O’Regan, Morse Theoretic Aspects of p–Laplacian Type Oper-ators, Mathematical Surveys and Monographs, Volume 161, American Mathematical Society, ProvidenceIsland, 2010.

(26) R.P. Agarwal, K. Perera and S. Pinelas, An Introduction to Complex Analysis, Springer, NewYork, 2011.

(27) S.K. Sen and R.P. Agarwal, , e, with MATLAB: Random and Rational Sequences with Scope inSupercomputing Era, Cambridge Scientific Publishers, Cambridge, 2011.

(28) R.P. Agarwal, L. Berezansky, E. Braverman and A. Domoshnitsky, Nonoscillation Theory ofFunctional Differential Equations with Applications, Springer, New York, 2012.


(29) A. Aral, V. Gupta and R. P. Agarwal, Applications of q–Calculus in Operator Theory, Springer,New York, 2013.

(30) R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Constant–Sign Solutions of Systems of IntegralEquations, Springer, in press.

Teaching and Other Experiences:

1. 44 years, various courses for B.Sc., M.Sc., B.E. and M.E.

2. U.G.C. Visiting Professor, Marathwada University, Aurangabad (February, 1979).

3. Visiting Scientist, Indian Institute of Science, Bangalore (September 1979).

4. Alexander Von Humboldt Foundation Fellow at der Ludwig -Maximilians Universitat, Munchen,with Prof. Dr. G. Hammerlin. (1980-81)

5. Visiting Professor, Instituto Matematico, Firenze, Italy (1981-82), with Prof. Roberto Conti.

6. Visiting Scientist, International Center for Theoretical Physics, Trieste (April 1982, April 1983).

7. Visiting Scientist, The University of Manitoba, Winnipeg, Canada (April-May 1983, April 1986).

8. Visiting Scientist, The University of Western Australia (April 1989).

9. Visiting Professor, University of Saskatchewan, Canada (April 1991).

10. Visiting Scientist, JSPS Cooperation Programmes, Japan (June 1991).

11. Visiting Professor, Politecnico di Milano, Milano, Italy (June 1995).

12. Visiting Professor, University of Delaware, USA (June 1997–May 1998).

13. Visiting Professor, Politecnico di Milano, Milano, Italy (December 2007).

14. Visiting Professor, University of Roma, Italy (May 2007).

15. Visiting Professor, Politecnico di Milano, Milano, Italy (June 2008).

16. KFUPM Chair Professor, King Fahd Univ. Petro. Minerals, Saudi Arabia (June 2010).

17. KFUPM Chair Professor, King Fahd Univ. Petro. Minerals, Saudi Arabia (May-July 2011).

18. Honorary Distinguished Professor, King Abdual Aziz University, Saudi Arabia (2011–).

Thesis Direction:

1. P.R. Krishnamoorthy, Boundary Value Problems for Higher Order Differential Equations, Ph.D.thesis, University of Madras, 1979.

2. E. Thandapani, On Continuous and Discrete Inequalities, Ph.D. thesis, University of Madras, 1981.

3. P.J.Y. Wong, On Two-Point Boundary Value Problems, Honours Project, National University ofSingapore, 1984.

4. F.C. Weng, On the Oscillatory Behaviour of Second Order Delay Differential Equations, HonoursProject, National University of Singapore, 1985.

5. G.L. Meng, Maximum Principles for Higher Order Differential Inequalities, Honours Project, Na-tional University of Singapore, 1987.


6. P.J.Y. Wong, Error Bounds for Quintic and Biquintic Spline Interpolation, Masters thesis, NationalUniversity of Singapore, 1987.

7. Ng Bee Cheow, On Gronwall’s Inequality and its Applications, Honours Project, National Universityof Singapore, 1988.

8. Goh Lee Leng, Uniqueness of Initial Value Problems, Honours thesis, National University of Singa-pore, 1988.

9. P.J.Y. Wong, Sharp Polynomial Interpolation Error Bounds for Derivatives and their Applications,Ph.D. thesis, National University of Singapore, 1991.

10. Lim Ee Tuo, Nonlinear Variation of Parameters for Differential and Difference Equations, HonoursProject, National University of Singapore, 1992.

11. Chan Kwok Leong, Opial Type Inequalities, Honours Project, National University of Singapore,1993.

12. Ngan Ngiap Teng, Gram Matrices, Inequalities and Applications, Honours Project, National Uni-versity of Singapore, 1994.

13. T.A. Smith, On Periodic Solutions of Nonlinear Hyperbolic Equations of the Fourth Order, Ph.D.thesis, Florida Institute of Technology, U.S.A. 2006.

Citations : Over 7000 in the following Journals and Series are known.

1. Acta Math. Hungar.2. Advances in Computational Mathematics3. Advances in Difference Equations4. Annales Polonici Mathematici5. Appl. Math. Comp.6. Appl. Math. Letters7. Applicable Analysis8. Archiv der Mathematik9. Arch. Math. (Brno)10. Astrophysics and Space Science11. Boundary Value Problems12. Bull. Austral. Math. Soc.13. Comm. Appl. Numer. Methods14. Computers Math. Applic.15. Computing16. CWI Monograph, North-Holland17. Czech. Math. Jour.18. de Gruyter Series in Nonlinear Analysis and Applications19. Differential and Integral Equations20. Dynamic Systems and Applications21. Fixed Point Theory and Applications22. Funkcialaj Ekvacioj23. IEEE Trans. on Automatic Control24. Int. Jour. Comp. Math.25. Int. Series of Numer. Math.26. Izv. Akad. Nauk. Arm. SSR, Mathematika27. Jour. Approximation Theory28. Jour. Comp. Appl. Math.


29. Jour. Comp. Physics30. Jour. Difference Equations and Appl.31. Jour. Differential Equations32. Jour. Inequalities and Applications33. Jour. Math. Anal. Appl.34. Jour. Mathl. Phyl. Sci.35. Mathematical and Computer Modelling36. Mathematics and its Applications, Kluwer Academic Publishers37. Mathematics in Science and Engineering, Academic Press, Inc.38. Mathematics Studies, North Holland39. Mathematika40. Nonlinear Analysis : TMA41. Nonlinear Times and Digest42. Numerische Mathematik43. Pitman Advanced Publishing Program44. Prentice Hall Series in Computational Mathematics45. Proc. Amer. Math. Soc.46. Proc. R. Soc. London47. Proc. Royal Society of Edinburgh48. Rocky Mountain J. Math.49. SIAM J. Math. Anal.50. SIAM Review51. Trans. Amer. Math. Soc.52. World Scientific Series in Applicable Analysis53. ZAA54. ZAMM

Refereed more than 5000 papers for the following Journals:

1. Journal of Differential Equations2. Journal Approximation Theory3. Journal of Mathematical Analysis and Applications4. Nonlinear Analysis5. Applicable Analysis6. Applied Mathematics Letters7. Applied Mathematics & Optimization8. Journal of Computational and Applied Mathematics9. Communications in Applied Numerical Methods10. Communications in Numerical Methods in Engineering11. Computers & Mathematics with Applications12. Advances in Computational Mathematics13. Dynamic Systems and Applications14. Journal of Difference Equations and Applications15. Archivum Mathematicum16. Mathematical and Computer Modelling17. Mathematische Nachrichten18. Japan Jour. Indusl. Appl. Math.19. International Journal of Math. and Mathl. Sciences20. International Journal of Numer. Methods Engg.21. Jour. Appl. Math. Simulation22. IEEE Trans. Automatic Control23. Proc. Edinburgh Math. Soc.


24. Numer. Methods Partial Diff. Equns.25. Jour. Austral. Math. Soc.26. Trans. Amer. Math. Soc.

Service as a reviewer of research monographs: Refereed several research monographs for KluwerAcademic, Springer–Verlag and World Scientific publishers. I have also written reviews for several mono-graphs in the journal SIAM Reviews.

Member of the Editorial Boards:

1. Editor-in-Chief, Journal of Inequalities and Applications, Springer, U.S.A.

2. Editor-in-Chief, Advances in Difference Equations, Springer, U.S.A.

3. Editor-in-Chief, Boundary Value Problems, Springer, U.S.A.

4. Editor-in-Chief, Fixed Point Theory and Applications, Springer, U.S.A.

5. Editor, Nonlinear Analysis: Theory, Methods and Applications, Elesiver, The Netherlands (till2012)

6. Editor, Nonlinear Analysis: Real World Applications, Elesiver, The Netherlands (till 2012)

7. Senior Editor, Applied Mathematics and Computation, Elsevier, The Netherlands.

8. Editor, Series in Mathematical Analysis and Applications, Gordon and Breach, U.K.

9. Editor, World Scientific Series in Applicable Analysis, World Scientific, Singapore.

10. Editor, Far East Journal of Mathematical Sciences, Pushpa Publishing House, India.(till 2008)

11. Associate Editor, Advances in Mathematical Sciences and Application, Japan.

12. Honorary Editor, Applicable Analysis, Gordon and Breach, U.K. (till 2012)

13. Associate Editor, Applied Mathematics Letters, Elsevier, The Netherlands.(till 2012)

14. Associate Editor, Archivum mathematicum, Masaryk Univ., Brno, Czech Rep. (till 2007)

15. Associate Editor, Communications in Applied Analysis, Dynamic Publishers, U.S.A.

16. Associate Editor, Communications in Applied Nonlinear Analysis, International Publications, U.S.A.(till 2012)

17. Associate Editor, Communications of the Korean Mathematical Society, Korea.(till 2010)

18. Associate Editor, Computers and Mathematics with Applications, Elsevier, The Netherlands.(till2012)

19. Associate Editor, Dynamics of Continuous, Discrete and Impulsive Systems, University of Waterloo,Canada.

20. Associate Editor, Dynamics of Continuous, Discrete and Impulsive Systems (series B, AppliedMathematics), University of Waterloo, Canada.(till 2008)

21. Associate Editor, Facta Universitatis: Mathematics and Informatics, University of Nis, Yugoslavia.

22. Associate Editor, Functional Differential Equations, The Research Institute, College of Judea andSamaria, Israel.


23. Associate editor, International Journal of Applied Mathematics, Academic Publications, Bulgaria.

24. Associate Editor, International Journal of Computational and Numerical Analysis and Applications,Academic Publishers, Bulgaria

25. Associate Editor, International Journal of Computer Mathematics, Gordon and Breach, U.K.(till2009)

26. Associate Editor, International Journal of Differential Equations and Applications, Academic Pub-lications, Bulgaria.

27. Associate Editor, Journal of Inequalities in Pure and Applied Mathematics, Australia

28. Associate Editor, Journal of Mathematical Analysis and Applications, Academic Press, U.S.A (till2007)

29. Associate Editor, Journal of Nonlinear and Convex Analysis, Yokohama Publishers, Japan

30. Associate Editor, The Korean Journal of Computational and Applied Mathematics, Korea (till2010)

31. Associate Editor, Mathematical and Computer Modelling, Elsevier, The Netherlands. (till 2012)

32. Associate Editor, Mathematical Inequalities and Applications, Zagreb, Croatia.

33. Associate Editor, Mathematical Sciences Research Hot-Line, International Publications, U.S.A. (till2009)

34. Associate Editor, Memoirs on Differential Equations and Mathematical Physics, Publishing HouseGCI, Tiblisi, Republic of Georgia.

35. Associate Editor, Neural, Parallel and Scientific Computations, Dynamic Publishers, U.S.A.

36. Associate Editor, Nonlinear Differential Equations: Theory, Methods and Applications, AndhraUniversity, India.

37. Asociate Editor, Nonlinear Analysis Forum, Korea.

38. Associate Editor, Nonlinear Functional Analysis and Applications, Kyungnam University Press,Korea.

39. Associate Editor, Nonlinear Oscillations, The Publication of the Institute of Mathematics, NationalAcademy of Sciences of Ukraine, Ukraine

40. Associate Editor, PanAmerican Mathematical Journal, International Publications, U.S.A. (till,2012)

41. Associate Editor, Journal of Mathematical Control Science and Applications, International SciencePress, India.

42. Associate Editor, East Asian Mathematical Journal, The Busan Gyeongnam Mathematical Society,Korea.

Editorial Work:

1. Numerical Mathematics, Singapore, (with Y. M. Chow and S. J. Wilson) International Series ofNumerical Mathematics, Volume 86. Birkhauser Verlag, Basel, 1988, p. 526.


2. Recent Trends in Differential Equations, World Scientific Series in Applicable Analysis, Volume 1,1992, p.583.

3. Contributions in Numerical Analysis, World Scientific Series in Applicable Analysis, Volume 2,1993, p.475.

4. Inequalities and Applications, World Scientific Series in Applicable Analysis, Volume 3, 1994, p.592.

5. Advances in Difference Equations, Special issue: Computers and Mathematics with Applications,Pergaman - Press, Volume 28 Numbers 1-3 (1994), pp 1-332.

6. Dynamical Systems and Applications, World Scientific Series in Applicable Analysis, Volume 4,1995, p.700.

7. Recent Trends in Optimization Theory and Applications, World Scientific Series in ApplicableAnalysis, Volume 5, 1995, p.482.

8. Advances in Differential and Integral Inequalities, Special issue: Nonlinear Analysis: Theory, Meth-ods and Applications, Pergaman - Press, Volume 25 Numbers 9-10 (1995), pp 871-1078.

9. Computer Aided Geometric Design (with Ruibin Qu), Special issue: Neural, Perallel & ScientificComputations, Dynamic Publishers, Volume 5 Numbers 1-2 (1997), 1-296.

10. Positive Solutions of Nonlinear Problems, Special issue: Journal of Computational and AppliedMathematics, Elsevier, Volume 88 Number 1 (1998), pp 1-238.

11. Proceedings of Equadiff 9 (with J. Vosmansk’y), Special issue: Archivum mathematicum, MasarykUniversity, Volume 34 (1998), pp 1-226.

12. Proceedings of Equadiff 9 (with F. Neuman and J. Vosmansky), Stony Brook: Electronic PublishingHouse, 1998, p. 251.

13. Advances in Difference Equations II, Special issue: Computers and Mathematics with Applications,Pergaman Press, Volume 36 Numbers 10-12 (1998), 1-429.

14. Proceedings of the International Workshop on Difference and Differential Inequalities (with L. E.Persson and A. Zafer), Special issue: Mathematical Inequalities and Applications, Volume 1 Number3 (1998), 347-461.

15. Discrete and Continuous Hamiltonian Systems (with M. Bohner), Special issue: Dynamic Systemsand Applications, Volume 8 Numbers 3-4 (1999), 307-588.

16. Fixed Point Theory with Applications in Nonlinear Analysis (with Donal O’Regan), Special issue:Journal of Computational and Applied Mathematics, Elsevier, Volume 113 Numbers 1-2 (2000),1-412.

17. Integral and Integrodifferential Equations (with Donal O’Regan), Series in Mathematical Analysisand Applications, Gordon & Breach, Amesterdam, Volume 2, 2000, p. 326.

18. Lakshmikantham’s Legacy: A Tribute on his 75th Birthday, Special issue: Nonlinear Analysis:Theory, Methods and Applications, Pergaman - Press, Volume 40 Numbers 1-8 (2000), pp 1-661.

19. Nonlinear Operator Theory (with Donal O’Regan), Special issue: Mathematical and ComputationalModelling, Pergamon Press, Volume 32 Numbers 11-13 (2000), 1287-1528.

20. Advances in Difference Equations III (with Donal O’Regan), Special issue: Computers and Mathe-matics with Applications, Pergaman Press, Volume 42 Numbers 3-5 (2001), 273-754.


21. Orthogonal Systems and Applications (with G.V. Milovanovic), Special issue: Applied Mathematicsand Computation, Elsevier, Volume 128 Issues 2-3 (2002), 149-414.

22. Advances in Difference Equations IV (with Martin Bohner and Donal O’Regan), Special issue:Computers and Mathematics with Applications, Pergaman Press, Volume 45 Numbers 6-9 (2003),861-1468.

23. Advances in Integral Equations (with Donal O’Regan), Special issue: Dynamic Systems and Appli-cations, Dynamic Publishers, Volume 14 Number 1 (2005), 1-173.

24. Proceedings of the Conference Differential and Difference Equations and Applications (with K.Perera), Hindawi, 2006, p. 1237.

International Conferences: Participated and gave invited lectures in the following conferences

1. Approximate Methods for Navier - Stokes Problems (Paderborn 1979, Germany)

2. General Inequalities 3 (Oberwolfach 1981, Germany)

3. Operator Inequalities (Oberwolfach 1981, Germany)

4. Ordinary Differential Equations (Oberwolfach 1983, Germany)


6. International Conference on Qualitative Theory of Differential Equations (Edmonton 1984, Canada)

7. Trends in the Theory and Practice of Nonlinear Analysis (Texas 1984, U.S.A.)

8. EQUADIFF 6 (Brno 1985, Czechoslovakia)


10. International Conference on Optimization : Techniques and Applications (1987, Singapore)

11. International Conference on Functional Equations and Inequalities (Szczawnica, 1987, Poland)

12. International Conference on Numerical Mathematics (1988, Singapore)

13. International Symposiumon Asymptotic and Computational Analysis (Winnipeg 1989, Canada)


15. First World Congress of Nonlinear Analysts (Tampa, 1992, U.S.A.)

16. Second International Conference on Dynamic Systems and Applications (Atlanta 1995, U.S.A.)

17. First International Conference on Neural, Parallel and Scientific Computations (Atlanta 1995,U.S.A.)

18. Second International Conference on Difference Equations and Applications (Vesprem 1995, Hun-gary)


20. International Workshop on Difference and Differential Inequalities (Gebze, 1996, Turkey)

21. Second World Congress of Nonlinear Analysts (Athens, 1996, Greece)

22. Modelling and System Stability Investigations (Kiev, 1997, Ukraine)


23. EQUADIFF 9 (Brno 1997, Czechoslovakia)

24. Third Midwest-Southeastern Atlantic Joint Regional Conference on Differential Equations (Nashville,TN 1997, U.S.A)

25. The Centennial Celebration: A Century of mathematics and Statistics at Nebraska (Lincoln 1998,U.S.A)

26. Third International Conference on Dynamic Systems and Applications (Atlanta 1999, U.S.A.)

27. Third World Congress of Nonlinear Analysts (Catania, 2000, Italy)

28. Sixth International Conference on Difference Equations and Applications (Augsburg, 2001, Ger-many)

29. International Conference on Differential, Difference Equations and their Applications (Patras 2002,Greece)

30. Fourth International Conference on Dynamic Systems and Applications (Atlanta 2003, U.S.A.)

31. Fourth World Congress of Nonlinear Analysts (Orlando, 2004, USA)

32. The 24th Annual Southeastern-Atlantic Regional Conference on Differential Equations (Universityof Tennessee at Chattanooga, 2004, USA)

33. Fifth International Conference on Dynamic Systems and Applications (Atlanta 2007, U.S.A.)

34. Fifth World Congress of Nonlinear Analysts (Orlando, 2008, USA)

35. Boundary Value Problems (Santiago de Compostela, 2008, Spain)

36. Fourteenth International Conference on Difference Equations and Applications (Istanbul, 2008,Turkey)

37. EQUADIFF 12 (Brno 2009, Czech Republic)

38. International Conference on Differential and Difference Equations and Applications (Ponta Delgada2011, Portugal)

39. International Conference on Applied Analysis and Algebra (Istanbul 2012, Turkey)

40. 11th International Workshop on Dynamical Systems and Applications (Ankara 2012, Turkey)

41. The International Conference on Mathematical Inequalities and Nonlinear Functional Analysis withApplications (Cinju 2012, Korea)

42. Southeastern–Atlantic Regional Conference on Differential Equations (Georgia Southern University,USA)

43. International Conference on Applied Analysis and Mathematical Modelling (Istanbul 2013, Turkey)

44. International Conference on Anatolian Communications in Nonlinear Analysis (Bolu 2013, Turkey)

Colloquium Talks: Several Colloquium talks delivered at the following centers

1. Universitat Karlsruhe (Germany, 1979)2. der Universitat Munchen (Germany, 1979)3. Georg - August - Universitat Gottingen (Germany, 1980)4. Universitat Stuttgart (Germany, 1980)


5. Mathematisch Centrum Amsterdam (Holland, 1980)6. University Van Amsterdam (Holland, 1980)7. Universita Degli Studi Di Parma (Italy, 1980)8. Universita Degli Studi Di Firenze (Italy, 1980)9. University of Ioannina (Greece, 1980)10. Universitat Karlsruhe (Germany, 1981)11. der Universitat Munchen (Germany, 1981)12. Technische Hochschule Darmstadt (Germany, 1981)13. Universitat Osnabruck (Germany, 1981)14. Universitat Hannover (Germany, 1981)15. Universita Degli Studi Di Firenze (Italy, 1982)16. Georg - August - Universitat Gottingen (Germany, 1983)17. Johann Wolfgang Goethe - Universitat Frankfurt (Germany, 1983)18. Albert - Ludwigs - Universitat Freiburg (Germany, 1983)19. der Universitat Tubingen (Germany, 1983)20. Universita Degli Studi Di Trieste (Italy, 1983)21. Universita Degli Studi Di Trento (Italy, 1983)22. J. E. Purkne University Brno (Czechoslovakia, 1983)23. Comenius University Bratislava (Czechoslovakia, 1983)24. The University of Manitoba (Canada, 1983)25. The University of Manitoba (Canada, 1986)26. Scuola Normale Superiore, Pisa (Italy, 1987)27. Politechnica di Milano (Italy, 1987)28. Rheinisch - Westfalische Technische Hochschule Aachen (Germany, 1989)29. Universitat Karlsruhe (Germany, 1989)30. der Universitat Munchen (Germany, 1989)31. Georg - August - Universitat Gottingen (Germany, 1989)32. Johann Wolfgang Goethe - Universitat Frankfurt (Germany, 1989)33. University of Western Australia (Australia, 1989)34. Murdoch University (Australia, 1989)35. University of Dundee (U.K. 1989)36. Brunel, The University of West London (U.K. 1989)37. The University of Sussex (U.K. 1989)38. The University of Liverpool (U.K. 1989)39. University of Manchester (U.K. 1989)40. University of Cambridge (U.K. 1989)41. Oxford University (U.K. 1989)42. University of Saskatchewan (Canada, 1991)43. The University of Tokyo (Japan, 1991)44. Tohoku University (Japan, 1991)45. Nagoya University (Japan, 1991)46. Ehime University (Japan, 1991)47. Okayama University (Japan, 1991)48. Kagoshima University (Japan, 1991)49. Hiroshima University (Japan, 1991)50. RIMS, Kyoto University (Japan, 1991)51. der Universitat Munchen (Germany, 1995)52. Universita Degli Studi Di Firenze (Italy, 1995)53. Universita Degli Studi Di Trieste (Italy, 1995)54. Scuola Normale Superiore, Pisa (Italy, 1995)55. Politechnica di Milano (Italy, 1995)56. Universita Degli Studi Di Roma (Italy, 1995)


57. Universita Degli Studi Di Bologna (Italy, 1995)58. SISSA, Trieste (Italy, 1995)59. Universitat Augsburg (Germany, 1995)60. Institute of Mathematics, Ukrainian Acad. Sci, Kiev (Ukraine, 1997)61. University of Nebraska, Lincoln, Nebraska (USA, 1997)62. Auburn University, Auburn, Alabama (USA, 1997)63. Washington University, St. Louis (USA, 1997)64. Wake Forest University, Winston Salem (USA, 1998)65. Florida Institute of Technology, Melbourne (USA, 1998)66. University of Central Florida, Orlando (USA, 1998)67. North Carolina State University, Raleigh (USA, 1998)68. San Diego State University, San Diego (USA, 1998)69. University of Southern California, Los Angeles (USA, 1998)70. University of Missori, Rolla (USA, 2000)71. The University of Queensland, (Australia, 2000)72. University of Delaware, (USA 2000)73. Geogia Institute of technology, (USA, 2000)74. Auburn University, Auburn, Alabama (USA, 2005)75. The Hong Kong Polytechnic University, (Hong Kong, 2006)76. The University of Hong Kong, (Hong Kong, 2006)77. City University of Hong Kong, (Hong Kong, 2006)78. Howard University, (USA, 2006)79. Georgetown University, (USA, 2006)80. Western Kentucky University, (USA, 2006)81. Michigan Technological University, (USA, 2007)82. University of Rome, (Italy, 2008)83. Politechnica di Milano (Italy, 2008)84. Seattle University (USA, 2009)85. King Fahd University of Petroleum and Minerals (Saudi Arabia, 2009)86. Istanbul Technical University (Turkey, 2009)87. Middle East Technical University (Turkey, 2009)88. Cankaya University (Turkey, 2009)89. Osmangazi University (Turkey, 2009)90. Izmir University (Turkey, 2009)91. Universidade De Santiago De Compostela (Spain, 2010)92. King Abdulaziz University (Saudi Arabia, 2010)93. American University of Sharjah (Sharjah, 2010)94. United Arab Emirates University (Al-Ain, 2010)95. King Fahd University of Petroleum and Minerals (Saudi Arabia, 2010)96. King Abdulaziz University (Saudi Arabia, 2011)97. King Fahd University of Petroleum and Minerals (Saudi Arabia, 2011)98. Texas AM University-Corpus Christi (USA, 2012)


Contents

1 A New Class of Riemannian ManifoldsYavuz Selim Balkan 35

2 Estimating MS −ARCH Models Using Recursive MethodAhmed Ghezal 36

3 Approximation by q−Durrmeyer type Polynomials in Compact Disks in the Case q > 1Nazim Idrisoglu Mahmudov 37

4 Finite Groups Whose Intersection Graphs are PlanarSelcuk Kayacan 38

5 On Solving Some Functional EquationsDmitry V.Kruchinin and Vladimir V.Kruchinin 39

6 On Computing Some Topological IndicesMohamed Amine Boutiche 40

7 History Slip-Dependent Evolutionary Quasi-Variational Inequalities with Volterra In-tegral TermNouiri Brahim 41

8 Approximation Properties of Weighted Kantorovich Type Operators in a CompactDisksMustafa Kara and Nazm I.Mahmudov 42

9 A Derivative Formula Associated with Eisenstein SeriesAykut Ahmet Aygunes 43

10 General Result on Viscoelastic Wave Equation with Degenerate Laplace Operator ofKirchhoff-Type in RnZennir Khaled 44

11 Moore-Penrose Inverse and Partial IsometriesSafa Menkad 45

12 Multiplicity Result for the Hamiltonian SystemTacksunJung and Q-Heung Choi 46

13 One-Parameter Apostol-Bernoulli Polynomials and Apostol-Euler PolynomialsVeli Kurt 47

14 On p-Bernoulli NumbersMourad Rahmani 48

15 The Roots of a Dual Split QuaternionHesna Kabadayı 49

16 On Some Inequalities for Hadamard Product of Special Types of MatricesSeyda Ildan and Hasan Kose 50


17 Generalized Newton Transformation and its Application to Transversal SubmanifoldsAbdelmalek Mohammed 51

18 Multiple Positive Solutions for Elliptic Singular Systems with Hardy Sobolev Expo-nentsBenmansour Safia 52

19 A Collocation Method for Solution of the Nonlinear Lane-Emden type Equations inTerms of Generalized Bernstein PolynomialsAysegul Akyuz-Dascıoglu and Nese Isler Acar 53

20 GALA and GADP2 Comparison for the Scheduling Problem of Rm/Sijk/Cmax

Duygu Yilmaz Eroglu and H.Cenk Ozmutlu 54

21 Improved MIP Model for Parallel Machines’ Scheduling ProblemDuygu Yilmaz Eroglu and H.Cenk Ozmutlu 55

22 Multiple Positive Solutions for Elliptic Singular Systems with Cafarelli Kohn Nirem-berg ExponentsMatallah Atika 56

23 Positive Solution for a Singular Second-Order Discrete Three-Point Boundary ValueProblemNoor Halimatus Sa’diah Ismail and Mesliza Mohamed 57

24 Positive Solution to Fourth Order Three-Point Boundary Value ProblemM.Mohamed, M.S.M.Noorani, M.S.Jusoh, M.N.M.Fadzil and R.Saian 58

25 Existence of Positive Solutions for Non-Homogeneous BVPs of p-Laplacian DifferenceEquationsFatma Tokmak and Ilkay Yaslan Karaca 59

26 L2 Norm Deconvolution Algorithm Applied to Ultrasonic Phased Array Signal Pro-cessingAbdessalem Benammar, Redouane Drai and Ahmed Khechida 60

27 Multi-Soliton Solutions for Non-Integrable Equations: Asymptotic ApproachGeorgy A.Omel’yanov 61

28 On Interpolation Functions for the q-analogue of the Eulerian Numbers Associatedwith any CharacterMustafa Alkan and Yilmaz Simsek 62

29 Computation of p-values for Mixtures of GaussiansBurcin Simsek and Satish Iyengar 63

30 Nonclassical Appell PolynomialsRahime Dere and Yilmaz Simsek 64

31 Remarks on the Central Factorial NumbersYilmaz Simsek 65


32 Nodals Solutions of the Fourth Order Equations Involving Paneitz-Branson Operatorwith Critical Sobolev ExponentBoughazi Hichem 66

33 Bilinear Multipliers of Weighted Wiener Amalgam Spaces and Variable ExponentWiener Amalgam SpacesOznur Kulak and A.Turan Gurkanlı 67

34 Global Optimization Problem of Lipschitz Functions Using α-Dense CurvesDjaouida Guettal and Mohamed Rahal 68

35 Estimating 2-D GARCH Models by Quasi-Maximum LikelihoodSoumia Kharfouchi 69

36 An Approach Using Stream Ciphers Algorithm for Speech Encryption and DecryptionBelmeguenai Aissa, Mansouri Khaled and Lashab Mohamed 70

37 A Generalized Statistical Convergence for Sequences of Sets via IdealsOmer Kisi and Ekrem Savas 71

38 Some Embedding Questions for Weighted Difference SpacesLeili Kussainova and Ademi Ospanova 72

39 On (λ, I)−Statistical Convergence of Order α of Sequences of FunctionHacer Sengul and Mikail Et 73

40 Range Kernel Orthogonality of Generalized DerivationsMessaoudene Hadia 74

41 On Stancu Variant of q-Baskakov-Durrmeyer Type OperatorsP.N.Agrawal and A.Sathish Kumar 75

42 Generalised Baskakov Kantorovich OperatorsP.N.Agrawal and Meenu Goyal 76

43 Approximate Solutions of Fractional Order Boundary Value Problems by a NovelMethodAli Akgul 77

44 Some Power Series on Archimedean and Non-Archimedean FieldsFatma Calıskan 78

45 Existence and Monotone Iteration of Symmetric Positive Solutions for Integral Boundary-Value Problems with φ-Laplacian OperatorTugba Senlik and Nuket Aykut Hamal 79

46 Analytical Calculation of Partial Differential Equations Applied to Electrical Ma-chines With Ideal Halbach Permanent MagnetsMourad Mordjaoui, Ibtissam Bouloukza and Dib Djalel 80

47 Principal Functions of Differential Operators with Spectral Parameter in BoundaryConditionsNihal Yokus 81


48 Generalized Typically Real FunctionsS.Kanas and A.Tatarczak 82

49 The Abel-Poisson Summability of Fourier Series in a Banach Space with Respect toa Continuous Linear RepresentationSeda Ozturk 83

50 Existence of Solutions for Integral Boundary Value Problems in Banach SpacesFulya Yoruk Deren and Nuket Aykut Hamal 84

51 Existence and Uniqueness Solution of Electro-Elastic Antiplane Contact Problem withFrictionMohamed Dalah, Khoudir Kibeche, Amar Megrous, Ammar Derbazi and Soumia Ahmed Chao-

uache 85

52 Almost Convex Valued Perturbation to Time Optimal Control Sweeping ProcessesDoria Affane and Dalila Azzam-Laouir 86

53 Evolution Problem Governed by Subdifferential OperatorMustapha Yarou 87

54 Nonlinear Elliptic Problem Related to the Hardy Inequality with Singular Term atthe BoundaryB.Abdellaoui, K.Biroud, J.Davila and F.Mahmoudi 88

55 On Periodic Solutions of Nonlinear Differential Equations in Banach SpacesAbdullah Cavus, Djavvat Khadjiev and Seda Ozturk 89

56 Generalized α-ψ-Contractive type M Mappings of Integral TypeErdal Karapinar, P.Shahi and Kenan Tas 90

57 Caristi’s Fixed Point Theorem in Fuzzy Metric SpacesHamid Mottaghi Golshan 91

58 Determination of the Unknown Coefficient in Time Fractional Parabolic Equationwith Dirichlet Boundary ConditionsEbru Ozbilge and Ali Demir 92

59 On p-adic Ising Model with Competing Interactions on the Cayley TreeFarrukh Mukhamedov, Hasan Akın and Mutlay Dogan 93

60 A Spectral Domain Computational Technique Dedicated to Fault Detection in Induc-tion MachineA.Medoued, A.Lebaroud, O.Boudebbouz and D.Sayad 94

61 Some Results on Double Fuzzy Topogenous OrdersVildan Cetkin and Halis Aygun 95

62 Finding Fixed Points of Firmly Nonexpansive-Like Mappings in Banach SpacesFumiaki Kohsaka 96

63 A Fourth Order Accurate Approximation of the First and Pure Second Derivativesof the Laplace Equation on a RectangleA.A.Dosiyev and H.M.Sadeghi 97


64 On the Positive Solutions for the Boundary Value Problems at ResonanceUmmahan Akcan and Nuket Aykut Hamal 98

65 On Weighted Approximation of Multidimensional Singular IntegralsGumrah Uysal and Ertan Ibikli 99

66 On Hermite-Hadamard Type Inequalities for ϕ−Convex Functions via Fractional In-tegralsMehmet Zeki Sarıkaya and Hatice Yaldız 100

67 Behavior of Positive Solutions of a Multiplicative Difference EquationDurhasan Turgut Tollu, Yasin Yazlık and Necati Taskara 101

68 A New Generalization of the Midpoint Formula for n−Time Differentiable Mappingswhich are ConvexCetin Yıldız and M.Emin Ozdemir 102

69 Global Bifurcations of Limit Cycles in the Classical Lorenz SystemValery Gaiko 103

70 Curvature of Curves Parameterized by a Time ScaleSibel Pasalı Atmaca and Omer Akguller 104

71 Essential Norms of Products of Weighted Composition Operators and DifferentiationOperators Between Banach Spaces of Analytic FunctionsJasbir S.Manhas and Ruhan Zhao 105

72 On the Null Forms, Integrating Factors and First Integrals to Path EquationsIlker Burak Giresunlu and Emrullah Yasar 106

73 Commutativity of Lommel and Halm Differential EquationsMehmet Emir Koksal 107

74 Equivalence Between Some Iterations in CAT (0) SpacesKyung Soo Kim 108

75 On Certain Combinatoric Convolution Sums of Divisor FunctionsDaeyeoul Kim and Nazli Yildiz Ikikardes 109

76 Some Properties of the Genocchi Polynomials with the Variable [x]qJ.Y.Kang and C.S.Ryoo 110

77 Boundedness of Localization Operators on Lorentz Mixed Normed Modulation SpacesAyse Sandıkcı 111

78 p−Summable Sequence Spaces with Inner ProductsSukran Konca, Hendra Gunawan and Mochammad Idris 112

79 An Alternative Proof of a Tauberian Theorem for Abel Summability MethodIbrahim Canak and Umit Totur 113

80 Positive Periodic Solutions for a Nonlinear First Order Functional Dynamic Equationby a New Periodicity Concept on Time ScalesErbil Cetin and F.Serap Topal 114


81 Potential Flow Field Around a TorusRajai Alassar 115

82 On B−1-Convex Functions and Some InequalitiesGabil Adilov and Ilknur Yesilce 116

83 On the Global Behaviour of a Higher Order Difference EquationYasin Yazlik, D.Turgut Tollu and Necati Taskara 117

84 Identifying an Unknown Time Dependent Coefficient for Quasilinear Parabolic Equa-tionsFatma Kanca and Irem Baglan 118

85 On Special Semigroup Classes and Congruences on Some Semigroup ConstructionsSeda Oguz and Eylem Guzel Karpuz 119

86 The Rate of Pointwise Convergence of q−Szasz OperatorsTuncer Acar 120

87 Some Properties of Cohomology Groups for GraphsOzgur Ege and Ismet Karaca 121

88 Stability with Respect to Initial Time Difference for Generalized Delay DifferentialEquationsRavi Agarwal and Snezhana Hristova 122

89 On Ramanujan’s Summation Formula, his General Theta Function and a Generaliza-tion of the Borweins’ Cubic Theta FunctionsChandrashekar Adiga 123

90 L∞ Error Estimate of Parabolic Variational Inequality Arising of the Pricing of Amer-ican OptionS.Madi, M.Hariour and M.C.Bouras 124

91 The Smoothness of Convolutions of Zonal Measures on Compact Symmetric SpacesSanjiv Kumar Gupta and Kathryn Hare 125

92 A Tauberian Theorem for the Weighted Mean Method of Summability of Sequencesof Fuzzy NumbersZerrin Onder, Sefa Anıl Sezer and Ibrahim Canak 126

93 Asymptotic Constancy for a System of Impulsive Delay Differential EquationsFatma Karakoc and Huseyin Bereketoglu 127

94 An Extension w with rankw = 3 of a Valuation v on a Field K with rankv = 2 to K(x)Figen Oke 128

95 Inclusions Between Weighted Orlicz SpaceAlen Osanclıol 129

96 On the Some Graph Parameters for Special GraphsNihat Akgunes, Ahmet Sinan Cevik and Ismail Naci Cangul 130


97 A Note on the Dirichlet-Neumann First Eigenvalue of a Family of Polygonal Domainsin R2

A.R.Aithal and Acushla Sarswat 131

98 An Approach to the Numerical Verification of Solutions for Variational InequalitiesC.S.Ryoo 132

99 Local Rings and Projective Coordinate SpacesFatma Ozen Erdogan and Suleyman Ciftci 133

100An Improved Numerical Solution of the Singular Boundary Integral Equation of theCompressible Fluid Flow Around Obstacles Using Modified Shape FunctionsLuminita Grecu 134

101New Aspects of Calculating Volumes in EnDaniela Bittnerova and Daniela Bımova 135

102Applications of an Alternative Methods for Volumes of Solids of RevolutionDaniela Bımova and Daniela Bittnerova 136

103On Certain Sums of Fibonomial CoefficientsEmrah Kılıc and Aynur Yalcıner 137

104Null Generalized Helices of a Null Frenet Curve in L4

Esen Iyigun 138

105Geometrical Methods and Numerical Computations for Prey-Predator Lotka-VolterraSystemsAdela Ionescu, Romulus Militaru and Florian Munteanu 139

106Fractional Calculus Model of Dengue EpidemicMoustafa El-Shahed 140

107 Zagreb Co Indices and Augmented Zagreb Index and its Polynomials of Phenyleneand Hexagonal SqueezeP.S.Ranjini, V.Lokesha and Usha.A 141

108 A Note on Class Numbers of Real Quadratic Fields with Certain Fundamental Dis-criminantsAyten Pekin 142

109On Three Dimensional Dynamical Systems on Time ScalesElvan Akın 143

110On the Difference Equation System xn+1 = 1+ynyn

, yn+1 = 1+ynxn

Necati Taskara, Durhasan Turgut Tollu and Yasin Yazlik 144

111The Binomial Transforms of Tribonacci and Tribonacci-Lucas SequencesNazmiye Yilmaz and Necati Taskara 145

112On the Random Functional Central Limit Theorems with Almost Sure Convergencefor SubsequencesZdzislaw Rychlik 146


113 Some Fixed Point Theorems for a Pair of Mappings in Complex Valued b-MetricSpacesAiman Mukheimer 147

114Some Characterizations of Slant Curves on Unit Dual Sphere S2

Seda Oral and Mustafa Kazaz 148

115On Solving Some Partial Differential EquationsUmit Sarp and Sebahattin Ikikardes 149

116Some Spectrum Properties in C∗- AlgebrasNilay Sager and Hakan Avcı 150

117 On Function Spaces with Fractional Fourier Transform in the Weighted LebesgueSpacesErdem Toksoy and Ayse Sandıkcı 151

118Some Convergence Results for Modified SP-Iteration Scheme in Hyperbolic SpacesAynur Sahin and Metin Basarır 152

119Characterization of W p−type of Spaces Involving Fractional Fourier TransformS.K.Upadhyay and Anuj Kumar 153

120 Rates of Convergence for an Estimator of a Density Function Based on HermitePolynomialsElif Ercelik and Mustafa Nadar 154

121Estimation of Reliability in Multicomponent Stress-Strength Model Based on Marshall–Olkin Weibull DistributionMustafa Nadar and Fatih Kızılaslan 155

122Some New Results on The Π−Regularity of Some MonoidsAhmet Emin and Fırat Ates 156

123On Traveling Wave Solutions of Fractional Differential EquationsSerife Muge Ege and Emine Mısırlı 157

124On the Oscillation of Second Order Nonlinear Neutral Dynamic Equations on TimeScalesElvan Akın, Can Murat Dikmen and Said Grace 158

125A Collocation Approach to Parabolic Partial Differential EquationsKubra Erdem Bicer and Salih Yalcınbas 159

126From Simplicial Homotopy to Crossed Module HomotopyI.Ilker Akca and Kadir Emir 160

127On Algebraic Semigroup and Graph-Theoretic Properties of a New GraphAhmet Sinan Cevik, Eylem Guzel Karpuz and I.Naci Cangul 161

128Embeddability and Grobner-Shirshov Basis TheoryEylem Guzel Karpuz 162


129An Application of Fixed Point Theorems to a Problem for the Existence of Solutionsof a Nonlinear Ordinary Differential Equations of Fractional OrderMasashi Toyoda 163

130A Numerical Solution for Vibrations of an Axially Moving BeamDuygu Donmez Demir and Erhan Koca 164

131Some Principal Congruence Subgroups of the Extended Hecke Groups and Relationswith Pell-Lucas NumbersZehra Sarıgedik, Sebahattin Ikikardes and Recep Sahin 165

132On the Metric Geometry and Regular PolyhedronsTemel Ermis and Rustem Kaya 166

133On the Addition of Collinear Points in Some PK-PlanesBasri Celik and Abdurrahman Dayioglu 167

134Local Stability Analysis of Strogatz Model with Two DelaysSertac Erman and Ali Demir 168

135Weighted Statistical Convergence in Intuitionistic Fuzzy Normed SpacesSelma Altundag and Esra Kamber 169

136 Sturm Comparison Theorems for Some Elliptic Type Equations with Damping andExternal Forcing TermsSinem Sahiner, Emine Mısırlı and Aydın Tiryaki 170

137 A Note on Solutions of the Nonlinear Fractional Differential Equations via the Ex-tended Trial Equation MethodMeryem Odabasi and Emine Misirli 171

138On Quantum Codes Obtained From Cyclic Codes Over F2 + uF2 + u2F2 + · · ·+ umF2

Abdullah Dertli, Yasemin Cengellenmis and Senol Eren 172

139On Some Functions Mapping the Zeros of Ln(x) to the Zeros of L′

n(x)Nihal Yılmaz Ozgur and Oznur Oztunc 173

140Finite Blaschke Products and R-Bonacci PolynomialsNihal Yılmaz Ozgur, Oznur Oztunc and Sumeyra Ucar 174

141 Convergence of Nonlinear Singular Integral Operators to the Borel DifferentiableFunctionsHarun Karsli and Ismail U.Tiryaki 175

142Regularization of an Abstract Class of Ill-Posed ProblemsDjezzar Salah and Benmerai Romaissa 176

143Decompositions of Soft ContinuityAhu Acıkgoz and Nihal Tas 177

144Lacunary Statistical Convergence of Double Sequences in Topological GroupsEkrem Savas 178


145On Fuzzy Pseudometric SpacesElif Aydın and Servet Kutukcu 179

146On Fixed Points of Extended Hecke GroupsBilal Demir and Ozden Koruoglu 180

147New Lagrangian Forms of Modified Emden Equation by Jacobi MethodGulden Gun Polat and Teoman Ozer 181

148Fixed Point Theorems for ψ-Contractive Mappings on Modular SpaceEkber Girgin and Mahpeyker Ozturk 182

149Convexity and Schur Convexity on New MeansV.Lokesha, U.K.Misra and Sandeep Kumar 183

150On Radial Signed GraphsGurunath Rao Vaidya, P.S.K.Reddy and V.Lokesha 184

151Delta and Nabla Discrete Fractional Gruss Type InequalityA.Feza Guvenilir 185

152 On Tame Extensions and Residual Transcendental Extensions of a Valuation withrankv = nBurcu Ozturk and Figen Oke 186

153Time Series Forecasting with Grey ModellingSeval Ene and Nursel Ozturk 187

154 Periodic Solution of Predator-Prey Dynamic Systems with Beddington-DeAngelisType Functional Response and ImpulsesAyse Feza Guvenilir, Billur Kaymakcalan and Neslihan Nesliye Pelen 188

155Approximation Properties of Kantorovich-Stancu Type Generalization of q-Bernstein-Schurer-Chlodowsky Operators on Unbounded DomainTuba Vedi and Mehmet Ali Ozarslan 189

156Use of Golden Section in MusicSumeyye Bakım 190

157On Analysis of Mathews-Lakshmanan Oscillator Equation via Nonlocal Transforma-tion and Lagrangian-Hamiltonian DescriptionOzlem Orhan and Teoman Ozer 191

158 On Singularities of the Galilean Spherical Darboux Ruled Surface of a Space Curvein the Pseudo-Galilean Space G1

3

Tevfik Sahin and Murteza Yılmaz 192

159Existence of Positive Solutions for Second Order Semipositone Boundary Value Prob-lems on the Half-LineF.Serap Topal and Gulsah Yeni 193

160Some Congruent Number FamiliesRefik Keskin and Ummugulsum Ogut 194


161On Some Fourth-Order Diophantine EquationsMerve Guney Duman and Refik Keskin 195

162Characteristic Subspaces of Finite Rank OperatorsMohamed Najib Ellouze 196

163Fixed Point Theory in WC-Banach AlgebrasBilel Mefteh 197

164 Oscillation and Nonoscillation Criteria for Second Order Generalized DifferenceEquationsYasar Bolat 198

165 On Generalizations of Some Inequalities Containing Diamond-Alpha Integrals andApplicationsBillur Kaymakcalan 199

166 On Reciprocity Law of the Y (h, k) Sums Associated with PDE’s of the Three-TermPolynomial RelationsElif Cetin, Yilmaz Simsek and Ismail Naci Cangul 200

167 Permutation Method for a Class of Singularly Perturbed Discrete Systems withTime-DelayTahia Zerizer 201

168 Existence of Minimal and Maximal Solutions for Quasilinear Elliptic Equation withNonlocal Boundary Conditions on Time-ScalesMohammed Derhab and Mohammed Nehari 202

169Application of Filled Function Method in Chemical Control of PestsAhmet Sahiner, Meryem Oztop, Gulden Kapusuz and Ozan Demirozer 203

170A New Approach to the Filled Function Method for Non-smooth ProblemsNurullah Yilmaz and Ahmet Sahiner 204

171 Determining of the Achievement of Students by Using Classical and Modern Opti-mization TechniquesAhmet Sahiner and Raziye Akbay 205

172Fuzzy Logic Approach to an UH-1 Helicopter Fuel Consumption and Calculation ofPower ProblemAhmet Sahiner and Reyhane Ercan 206

173 Determination of Effects of Brassinosteroid Applications on Secondary MetaboliteAccumulation in Salt Stressed Peppermint (Mentha piperita L.) by Modern Opti-mization TecniquesAhmet Sahiner, Tuba Yigit, Ozkan Coban and Nilgun Gokturk Baydar 207

174On a Completeness Property of C(X) Equipped with a Set-Open TopologySmail Kelaiaia 208

175Existence of Solutions of a Class of Second Order Differential InclusionsD.Azzam-Laouir and F.Aliouane 209


176Applications of Generalized Fibonacci Autocorrelation Sequences Γk,n (τ)∞τSibel Koparal and Nese Omur 210

177The Computer Simulation of Nuclear Magnetic Resonance Hyperfine Structure Con-stant for AB2, A2B2 and A2B3 Systems Containing Some Organic Molecules with Spin12 Using Jacobi ProgrammeHuseyin Ovalıoglu, Adnan Kılıc and Handan Engin Kırımlı 211

178The Computer Simulation of Nuclear Magnetic Resonance Hyperfine Structure Con-stant for ANX, ABC and A3BC Systems Containing Some Organic Molecules withSpin 1

2 Using Jacobi ProgrammeHuseyin Ovalıoglu, Handan E.Kırımlı, Cengiz Akay and Adnan Kılıc 212

179 Necessary and Sufficient Conditions for First Order Differential Operators to beAssociated with a Disturbed Dirac Operator in Quaternionic AnalysisUgur Yuksel 213

180Theoretical Investigation of Substituent Effect on the Carbonyl Stretching VibrationIlhan Kucuk and Aslı Ayten Kaya 214

181Modeling of the Optical Properties of the CdS Thin Films by Using Artificial NeuralNetworkAslı Ayten Kaya, Kadir Erturk, Nil Kucuk and Ilker Kucuk 215

182 Nonprinciple Solutions and Extensions of Wong’s Oscillation Criteria to ForcedSecond-Order Impulsive and Delay Differential EquationsAbdullah Ozbekler and Agacık Zafer 216

183 Modeling of Exposure Buildup Factors for Concrete Shielding Materials up to 10mfp Using Generalized Feed-Forward Neural NetworkNil Kucuk, Vishwanath P.Singh and N.M.Badiger 217

184Calculation of Gamma-Ray Exposure Buildup Factors for Some Biological SamplesNil Kucuk, Vishwanath P.Singh and N.M.Badiger 218

185Determination of Thermoluminescence Kinetic Parameters of ZnB2O4: La PhosphorsNil Kucuk, A.Halit Gozel, Mustafa Topaksu and Mehmet Yuksel 219

186 Improved Numerical Radius and Spectral Radius Inequalities for OperatorsFuad Kittaneh and Amer Abu-Omar 220

187n-Dimensional Sobolev type spaces involving Chebli-Trimeche TransformMourad Jelassi 221

188 A Fixed Point Theorem for Multivalued Mappings with δ-Distance on CompleteMetric SpaceOzlem Acar and Ishak Altun 222

189 Existence of Solutions of α ∈ (2, 3] Order Fractional Three Point Boundary ValueProblems with Integral ConditionsSinem Unul and N.I.Mahmudov 223

190Vector-Valued Variable Exponent Amalgam SpacesIsmail Aydın 224


191Soliton Solutions of Sawada–Kotera Equation by Hirota MethodEsra Karatas and Mustafa Inc 225

192Certain Quasi-Cyclic Codes which are Hadamard CodesMustafa Ozkan and Figen Oke 226

193Pointwise Convergence of Derivatives of New Baskakov-Durrmeyer-Kantorovich TypeOperatorsGulsum Ulusoy, Ali Aral and Emre Deniz 227

194On the High Order Lipschitz Stability of Inverse Nodal Problem for String EquationEmrah Yılmaz and Hikmet Koyunbakan 228

195 Positive Solutions of a Boundary Value Problem with Derivatives in the NonlinearTermPatricia J.Y.Wong 229

196One Step Iteration Scheme for Two Multivalued Mappings in CAT(0) SpacesIzhar Uddin and M.Imdad 230

197A Variant Akaike Information Criterion for Mixture Autoregressive Model SelectionFaycal Hamdi 231

198Zagreb Polynomials of Three graph OperatorsA.R.Bindusree, V.Lokesha, I.Naci Cangul and P.S.Ranjini 232

199A Note on the Moment Estimate for Stochastic Functional Differential EquationsYoung-Ho Kim 233

200 Issues Optimization of Public AdministrationCanybec Sulayman and Gulnar Suleymanova 234

201Jacobi Orthogonal Approximation with Negative Integer and its ApplicationZhang Xiao-yong and Wan Zheng-su 235

202Existence Results for Nonlinear Impulsive Fractional Differential Equations with p−Laplacian OperatorIlkay Yaslan Karaca and Fatma Tokmak 236

203A Relation Between the Lefschetz Fixed Point Theorem and the Nielsen Fixed PointTheorem in Digital ImagesIsmet Karaca 237

204 Second Order Nonlinear Boundary Value Problems with Integral Boundary Condi-tions on Time ScalesF.Serap Topal and Arzu Denk Oguz 238

205Existence of a Solution of Integral Equations via Fixed Point TheoremSelma Gulyaz 239

206Triangular and Square Triangular NumbersArzu Ozkoc 240


207Approximation Methods on a Complete Geodesic SpaceYasunori Kimura 241

208Fixed Point Results for α-Admissible Multivalued F−ContractionsGonca Durmaz and Ishak Altun 242

209Advances on Fixed Point TheoryErdal Karapınar 243

210Fixed Point Theorems for a Class of α-Admissible Contractions and Applications toBoundary Value ProblemInci M.Erhan 244

211Feng-Liu Type Fixed Point Theorems for Multivalued MappingsGulhan Mınak and Ishak Altun 245

212Qualitative Analysis for the Differential Equation Associated to the Dynamic Modelfor an Access Control StructureDaniela Coman, Adela Ionescu and Sonia Degeratu 246

213Zagreb Indices of Double GraphsAysun Yurttas, Muge Togan and Ismail Naci Cangul 247

214Several Zagreb Indices of Subdivision Graphs of Double GraphsMuge Togan, Aysun Yurttas and Ismail Naci Cangul 248

215On the Solutions of the Diophantine Equation xn + p · yn = p2 · znCaner Agaoglu and Musa Demirci 249

216 A Weak Contraction Principle in Partially Ordered Cone Metric Space with ThreeControl FunctionsBinayak S.Choudhury, L.Kumar, T.Som and N.Metiya 250

217On the Diophantine Equation (20n)x + (99n)y = (101n)z

Gokhan Soydan, Musa Demirci and Ismail Naci Cangul 251

218Halpern Type Iteration with Multiple Anchor Points in a Hadamard SpaceYasunori Kimura and Hideyuki Wada 252

219Multimaps in Fixed Point Theorems in Terms of Measure of NoncompactnessMehdi Asadi 253

220Pointwise Approximation in Lp Space by Double Singular Integral OperatorsMine Menekse Yılmaz, Gumrah Uysal and Ertan Ibikli 254

221Some Tauberian Remainder Theorems for Iterations of Weighted Mean Methods ofSummabilitySefa Anıl Sezer and Ibrahim Canak 255

222On The Semi-Fredholm SpectrumArzu Akgul 256

223Critical Fixed Point Theorems in Banach Algebras Under Weak Topology FeaturesA.Ben Amar and A.Tlili 257


224 Modeling of Effect of the Components of Distance Education in Achievement ofStudentsHamit Armagan, Tuncay Yigit and Ahmet Sahiner 258

225On the Weighted Integral Inequalities for Convex FunctionMehmet Zeki Sarıkaya and Samet Erden 259


1 A New Class of Riemannian ManifoldsYavuz Selim Balkan

In this study, we introduce a new class of (2n+ 1)−dimensional Riemannian manifolds. Such type man-ifolds are called almost contact metric manifolds which have ϕ−recurrent τ−curvature tensor. We inves-tigate some curvature properties of this type manifold. We obtain that these manifolds are η−Einsteinmanifolds under some algebraic conditions.

References

[1] De U. C., Yıldız A. and Yalınız A. F., On ϕ−recurrent Kenmotsu manifolds, Turkish J. Math. 32(2008), 1-12.

[2] De U. C. and Guha N., On generalized recurrent manifolds, J. Nat. Acad. Math. India 9 (1991), 85-92.

[3] Tripathi M. M. and Gupta P., τ−curvature tensor on a semi-Riemannian manifold, J. Adv. Math.Stud., 4 (2011), no. 1, 117-129.

Duzce University, Faculty of Arts and Sciences, Department of Mathematics, Duzce, Turkiye, [email protected]


2 Estimating MS − ARCH Models Using Recursive MethodAhmed Ghezal

In this note we offer model more realistically the variability of financial time series. Markov-switchingautoregressive conditional heteroskedasticity (MS −ARCH) model introduced by Cai that incorporatesthe features of both Hamilton and Engle ARCH model to study the matter of volatility persistence in themonthly excess revenues. The matter can be resolved by taking into account occasional transformationsin the asymptotic variance of the MS − ARCH process that cause the Pseudomonas persistence of thevolatility process. One of the interesting issues of financial time series volatility relates to the persistenceof shocks to the variance. A common finding using high-frequency financial data concerns the apparentpersistence implied by the estimates for the conditional variance functions. In these models, the param-eters are allowed to depend on an unobservable time-homogeneous and stationary Markov chain withfinite state space. The statistical inference for these models is rather difficult due to the dependence tothe whole regime path. We propose a recursive algorithm for parameter estimation in MS − ARCH.The proposed method which is useful for long time series as well as for data available in real time. Themain idea is to use the maximum likelihood estimation (MLE) method and from this develop a recursiveExpectation-Maximization (EM) algorithm.

References

[1] A. Aknouche, Recursive online EM estimation of mixture autoregressions. Journal of Statistical Com-putation and Simulation, Vol. 83, No. 2 (2013), 370− 383,

[2] J. Cai, A Markov model of switching regime ARCH. J. Bus. Econ. Stat. 12 (1994), 309− 316,

[3] O. Cappe, E. Moulines, Online expectation maximization algorithm for latent data models, J. R.Statist. Soc. B 71 (2009), 593− 613,

[4] I. Conllings, V. Krishnamurthy, J. B. Moore, Online identification of hidden Markov models viarecursive prediction error techniques, IEEE Trans. Signal Process. 42 (1994), 3535− 3539,

[5] J. D. Hamilton, R. Susmel, Autoregressive conditional heteroskedasticity and changes in regime. J.Econ 64 (1994), 307− 333,

[6] U. Holst, G. Lindgren, Recursive estimation in mixture models with Markov regime, IEEE Trans.Inform. Theory 37 (1991), 1683− 1690,

[7] U. Holst, G. Lindgren, J. Holst, M. Thuvesholmen, Recursive estimation in switching autoregressionswith a Markov regime, J. Time Ser. Anal. 15 (1994), 489− 506,

University of Constantine 1, Algeria, Faculty of Science, Department of Mathematics, [email protected]


3 Approximation by q−Durrmeyer type Polynomials in Com-pact Disks in the Case q > 1Nazim Idrisoglu Mahmudov

In this talk, we discuss approximation properties of the complex q-Durrmeyer type operators in thecase q > 1. Quantitative estimates of the convergence, the Voronovskaja type theorem and saturation ofconvergence for complex q-Durrmeyer type polynomials attached to analytic functions in compact diskswill be given. In particular, we show that for functions analytic in z ∈ C : |z| < R, R > q, the rate ofapproximation by the q-Durrmeyer type polynomials (q > 1) is of order q−n versus 1/n for the classical(q = 1) Durrmeyer type polynomials. Explicit formulas of Voronovskaya type for the q-Durrmeyer typeoperators for q > 1 are also given.

References

[1] R. P Agarwal and V. Gupta, On q-analogue of a complex summation-integral type operators incompact disks, Journal of Inequalities and Applications, 2012, 2012:111.

[2] G. A. Anastassiou and S.G. Gal, Approximation by Complex Bernstein-Durrmeyer Polynomials inCompact Disks, Mediterr. J. Math., 7 (2010), No. 4, 471-482.

[3] Andrews G E, Askey R, Roy R. Special functions. Cambridge: Cambridge University Press; 1999.

[4] A. Aral, V. Gupta, R.P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, NewYork, 2013.

[5] M-M. Derriennic , Modified Bernstein polynomials and Jacobi polynomials in q-calculus, RendicontiDel Circolo Matematico Di Palermo, Serie II 2005; 76(Suppl.):269–290.

[6] S. G. Gal, Overconvergence in Complex Approximation, Springer New York Heidelberg DordrechtLondon, 2013.

[7] S. G. Gal, Approximation by complex genuine Durrmeyer type polynomials in compact disks, Appl.Math. Comput., 217(2010), 1913–1920.

[8] S. G. Gal, V. Gupta, N. I. Mahmudov, Approximation by a complex q-Durrmeyer type operator,Ann Univ Ferrara, (2012) 58:65–87.

[9] N. I. Mahmudov, Approximation by Genuine q-Bernstein-Durrmeyer Polynomials in Compact Disksin the case q > 1. Abstract and Applied Analysis.

[10] N. I. Mahmudov, Approximation properties of complex q-Szasz-Mirakjan operators in compact disks.Comput. Math. Appl. 60, 1784–1791 (2010)

[11] N. I. Mahmudov, Approximation by genuine q -Bernstein-Durrmeyer polynomials in compact disks,Hacettepe Journal of Mathematics and Statistics, 40 (1) (2011), 77-89.

[12] N. I. Mahmudov, Approximation by Bernstein–Durrmeyer-type operators in compact disks, AppliedMathematics Letters, 24 (7) (2011), 1231-1238.

[13] S. Ostrovska, q-Bernstein polynomials and their iterates,. J. Approx. Theory, 123 (2003), 232–255.

Eastern Mediterranean University, Department of Mathematics, Gazimagusa, TRNC, Mersin 10, Turkey, nazim. [email protected]


4 Finite Groups Whose Intersection Graphs are PlanarSelcuk Kayacan

The intersection graph of a group G is an undirected graph without loops and multiple edges defined asfollows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge betweentwo distinct vertices H and K if and only if H ∩K 6= 1 where 1 denotes the trivial subgroup of G. In thistalk we characterize all finite groups whose intersection graphs are planar. Our methods are elementary.Among the graphs similar to the intersection graphs, we may count the subgroup lattice and the subgroupgraph of a group, each of whose planarity was already considered before in [2, 10, 11, 12, 13].

References

[1] Alonso, J.: Groups of order pqm with elementary abelian Sylow q-subgroups. Proc. Amer. Math.Soc. 65(1), 16–18 (1977)

[2] Bohanon, J.P., Reid, L.: Finite groups with planar subgroup lattices. J. Algebraic Combin. 23(3),207–223 (2006)

[3] Burnside, W.: Theory of groups of finite order. Dover Publications Inc., New York (1955). 2d ed

[4] Cole, F.N., Glover, J.W.: On Groups Whose Orders are Products of Three Prime Factors. Amer. J.Math. 15(3), 191–220 (1893)

[5] Gorenstein, D.: Finite groups, second edn. Chelsea Publishing Co., New York (1980)

[6] Holder, O.: Die Gruppen der Ordnungen p3, pq2, pqr, p4. Math. Ann. 43(2-3), 301–412 (1893)

[7] Le Vavasseur, R.: Les groupes d’ordre p2q2, p etant un nombre premier plus grand que le nombrepremier q. Ann. Sci. Ecole Norm. Sup. (3) 19, 335–355 (1902)

[8] Miller, G.A.: Groups having a small number of subgroups. Proc. Nat. Acad. Sci. U. S. A. 25, 367–371(1939)

[9] Rotman, J.J.: An introduction to the theory of groups, Graduate Texts in Mathematics, vol. 148,fourth edn. Springer-Verlag, New York (1995)

[10] Schmidt, R.: On the occurrence of the complete graph K5 in the Hasse graph of a finite group. Rend.Sem. Mat. Univ. Padova 115, 99–124 (2006)

[11] Schmidt, R.: Planar subgroup lattices. Algebra Universalis 55(1), 3–12 (2006)

[12] Starr, C.L., Turner III, G.E.: Planar groups. J. Algebraic Combin. 19(3), 283–295 (2004)

[13] Yaraneri, E.: Intersection graph of a module. J. Algebra Appl. 12(5), 1250,218, 30 pp. (2013)

Department of Mathematics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey, [email protected]


5 On Solving Some Functional EquationsDmitry V.Kruchinin and Vladimir V.Kruchinin

In this talk, we discuss some methods for solving functional equations based on generating functions.Particularly, using the notion of the composita and Lagrange inversion theorem, we present techniques forsolving the following functional equation A(x) = G(xA(x)α), where A(x), G(x) are generating functionswith G(0) 6= 0, and α is any real number. Also we give some examples.

References

[1] D. V. Kruchinin and V. V. Kruchinin, Application of a composition of generating functions for ob-taining explicit formulas of polynomials, J. Math. Anal. Appl., 404 (2013), 161–171,

[2] D. V. Kruchinin and V. V. Kruchinin, A method for obtaining generating functions for central coef-ficients of triangles, Journal of Integer Sequences., textbf15(12.9.3) (2012), 1–10,

[3] D. V. Kruchinin and V. V. Kruchinin, Explicit formulas for some generalized polynomials, AppliedMathematics and Information Sciences, 7(5) (2013), 2083–2088,

[4] R. P. Stanley, Enumerative Combinatorics 2, vol. 62 of Cambridge Studies in Advanced Mathematics,Cambridge Univ. Press, Cambridge, 1999,

[5] R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading,MA, 1989,

[6] G. P. Egorichev, Integral Representation and the Computation of Combinatorial Sums, Amer. Math.Soc. 1984,

[7] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, 1974.

Dmitry V. Kruchinin: Department of Complex Information Security, Tomsk State University of Control Systems andRadioelectronics, Tomsk, Russia, [email protected]

Vladimir V. Kruchinin: Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia, [email protected]

The reported study was partially supported by the Ministry of education and science of Russia, government order No1220 ”Theoretical bases of designing informational–safe systems”.


6 On Computing Some Topological IndicesMohamed Amine Boutiche

The Wiener index of a graph G = (V,E) defined as W (G) =∑

u,v⊆V (G)

dG(u, v) where dG(u, v) is a

distance between two vertices u, v ∈ V (G) (the minimum number of edges on a path in G between u andv), was introduced by Harold Wiener in 1947. In this talk, we show how to compute some of well-knowntopological indices; the Wiener and the Wiener Polarity Index for Sun Graphs.

References

[1] H. Deng, On the extremal Wiener polarity index of chemical trees, MATCH Commun. Math. Comput.Chem. (in press).

[2] H. Deng, H. Xiao, F. Tang, On the extremal Wiener polarity index of trees with a given diameter,MATCH Commun. Math. Comput. Chem. 63 (2010) 257–264.

[3] H. Deng, H. Xiao, The maximum Wiener polarity index of trees with k pendants, Appl. Math. Lett.23 (2010) 710–715.

[4] W. Du, X. Li, Y. Shi, Algorithms and extremal problem on Wiener polarity index, MATCH Commun.Math. Comput. Chem. 62 (2009) 235–244.

[5] I. Gutman, E. Estrada, Topological indices based on the line graph of the molecular graph, J. Chem.Inf. Comput. Sci. 36 (1996) 541–543.

[6] I. Gutman, L. Popovic, B.K. Mishra, M. Kaunar, E. Estrada, N. Guevara, Application of line graphsin physical chemistry. Predicting surface tension of alkanes, J. Serb. Chem. Soc. 62 (1997) 1025–1029.

[7] H. Hosoya, Mathematical and chemical analysis of Wiener’s polarity number, in: D.H. Rouvray,R.B. King (Eds.), Topology in Chemistry-Discrete Mathematics of Molecules, Horwood, Chichester,2002, p. 57.

[8] B. Liu, H. Hou and Y. Huang, On the Wiener polarity index of trees with maximum degree or givennumber of leaves, Comput. Math. Appl. 60 (2010) 2053–2057.

[9] I. Lukovits, W. Linert, Polarity-numbers of cycle-containing structures, J. Chem. Inf. Comput. Sci.38 (1998) 715–719.

[10] N. Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, FL, 1993.

[11] H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17–20.

Universite des sciences et de la Technologie Houari Boumediene, BP 32, El Alia 16111, Bab Ezzouar, Faculty ofMathematics, Department of Operations research, Algiers, Algeria, [email protected] or [email protected]

This work was supported by Scientific Research Project CNEPRU (OTMADS 3I), Project number B00220110019


7 History Slip-Dependent Evolutionary Quasi-Variational In-equalities with Volterra Integral TermNouiri Brahim

In this talk, we present and analyze a class of history slip-dependent evolutionary quasi-variationalinequalities with Volterra integal term. We prove the existence and uniqueness result, by using argumentsof evolutionary variational inequalities with voscosity and Banach’s fixed-point theorem. Next, we studythe dependence of the solution on the long-term memory and derive a convergence result. Finally, wepresent a number of concrete examples of frictional contact problems for which our results apply.

References

[1] N. Brahim. Etude theorique et numerique des phenomenes vibratoires lies au frottement sec des solidesdeformables. These de Doctorat en Sciences, Universite Hadj Lakhdar de Batna, Algerie, 2011.

[2] M. Sofonea and A. Matei. Variational inequalities with applications, A Study of Antiplane FrictionalContact Problems. Springer: New York, 2009.

[3] M. Sofonea and A. Rodriguez-Aros and J. M. Viano. A Class of Integro-Differential VariationalInequalities with Applications to Viscoelastic Contact. Mathematical and Computer Modelling, 41:1355–1369, 2005.

Laboratory of Computer Science and Mathematics, University of Laghouat, Raod of Ghardaıa, BP 37G, Laghouat(03000), Algeria, [email protected]

This work was supported by Thematic Agency of Rresearch in Sciences and Technology (ATRST) within the frameworkof the national projects of researches: 8-Sciences fundamental.


8 Approximation Properties of Weighted Kantorovich Type Op-erators in a Compact DisksMustafa Kara and Nazm I.Mahmudov

In this talk, we discuss approximation properties of the complex weighted Kantorovich Type operators.Quantitative estimates of the convergence, the Voronovskaja type theorem and saturation of convergencefor complex weighted Kantorovich polynomials attached to analytic functions in compact disks will begiven. In particular, we show that for functions analytic in z ∈ C : |z| < R, the rate of approximationby the weighted complex Kantorovich type operators is 1/n.

References

[1] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer, 1987.

[2] B. Della Vecchia, G. Mastroianni and J. Szabados, A weighted generalization of the classical Kan-torovich operator, Rend. Circ. Mat. Palermo (2), 82 (2010), 1-27

[3] B. Della Vecchia, G. Mastroianni and J. Szabados, A weighted generalization of the classical Kan-torovich operator.II Saturation, Mediter. J. Math., to appear.

[4] D. S. YU, Weighted approximation by modified Kantorovich-Bernstein operators, Acta Math. hungar.,141 (1-2) (2013), 132-149.

[5] Bernstein, S. N., Demonstration du theoreme de Weierstrass fondee sur le calcul de probabilites,Commun. Soc. Math. Kharkow, 13. No. 2, 1-2, (1912-1913).

[6] S.G. Gal, Approximation by Complex Bernstein and Convolution Type Operators, Series on Concreteand Applicable Mathematics, Vol. 8, World Scientific Publishing Co, 2009.

Eastern Mediterranean University, Department of Mathematics, Gazimagusa, TRNC, Mersin 10, Turkey, [email protected], [email protected]


9 A Derivative Formula Associated with Eisenstein SeriesAykut Ahmet Aygunes

In this talk, we construct a new formula which derives the modular functions of weight 8k+ 12 by usingthe modular functions of weight 4k + 4. Then we substitute Eisenstein series into our formula and weobtain some results. Also we investigate some properties of operators related to our derivative formula.

References

[1] T. M. Apostol, Modular functions and Dirichlet series in Number Theory, (Berlin, Heidelberg andNew York) Springer-Verlag (1976).

[2] A. A. Aygunes, A new operator related to generating modular forms and their applications, preprint.

[3] A. A. Aygunes, Derivative formulae for modular forms and their properties, preprint.

[4] A. A. Aygunes, Y. Simsek, H. M. Srivastava, A sequence of modular forms associated with higherorder derivative Weierstrass-type functions, preprint.

[5] E. Hecke, Mathematische Werke, Vandenhoeck & Ruprecht in Gottingen, 1983.

[6] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, New York (1993).

[7] S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184.

[8] A. Sebbar, A. Sebbar, Eisenstein Series and Modular Differential Equations, Canad. Math. Bull. 55(2011), 400-409.

[9] J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, New York, Heidelberg and Berlin,Springer-Verlag (1994).

Department of Mathematics, Faculty of Art and Science University of Akdeniz TR-07058 Antalya, Turkey, [email protected]

The authors are supported by the research fund of Akdeniz University.


10 General Result on Viscoelastic Wave Equation with Degen-erate Laplace Operator of Kirchhoff-Type in Rn

Zennir Khaled

We shall give general energy decay of solutions to viscoelastic wave equations of p−Laplacian in Kichhofftype. In order to compensate the lack of Poincare’s inequality in Rn and for wider class of relaxationfunctions, we are going to use weighted spaces.

References

[1] M. Abdelli and A. Benaissa, Energy decay of solutions of degenerate Kirchhoff equation with a weaknonlinear dissipation, Nonlinear Analysis, 69 (2008) ,1999-2008.

[2] Alabau-Boussouira, F. and Cannarsa, P., A general method for proving sharp energy decay rates formemory-dissipative evolution equations, C. R. Acad. Sci. Paris, Ser. I 347, 867-872 (2009).

[3] Arnold, V. I., Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1989.

[4] A. Benaissa, S. Mokeddem, Global existence and energy decay of solutions to the Cauchy problem fora wave equation with a weakly nonlinear dissipation, Abstr. Appl. Anal, 11(2004) 935-955.

[5] Brown, K.J.; Stavrakakis, N. M, Global bifurcation results for semilinear elliptic equations on all ofRn, Duke Math Journ, 85 (1996), 77?94.

[6] M.M. Cavalcanti, H.P. Oquendo, Frictional versus viscoelastic damping in a semilinear wave equa-tion, SIAM J. Control Optim. 42(4)(2003)1310–1324.

[7] Irena Lasiecka, Salim A. Messaoudi, and Muhammad I. Mustafa, Note on intrinsic decay rates forabstract wave equations with memory, JOURNAL OF MATHEMATICAL PHYSICS 54, 031504(2013).

[8] M. Kafini, uniforme decay of solutions to Cauchy viscoelastic problems with density, Elec. J. Diff.Equ Vol.2011 (2011)No. 93, pp. 1-9.

[9] M. Kafini and S. A. Messaoudi, On the uniform decay in viscoelastic problem in Rn, Applied Math-ematics and Computation 215 (2009) 1161-1169.

[10] M. Kafini, S. A. Messaoudi and Nasser-eddine Tatar, Decay rate of solutions for a Cauchy viscoelasticevolution equation, Indagationes Mathematicae 22 (2011) 103-115.

[11] G. Kirchhoff, Vorlesungen uber Mechanik,3rd ed., Teubner, Leipzig, (1983).

[12] karachalios, N.I; Stavrakakis, N.M, Existence of global attractor for semilinear dissipative wave equa-tions on Rn, J. Diff. Equ 157 (1999) 183-205.

[13] P. Martinez, A new method to obtain decay rate estimates for dissipative systems, ESAIM ControlOptimal. Calc. Var. 4(1999)419-444.

[14] Muhammad I. Mustafa and S. A. Messaoudi, General stability result for viscoelastic wave equations,JOURNAL OF MATHEMATICAL PHYSICS 53, 053702 (2012).

[15] J. E. Munoz Rivera, Global solution on a quasilinear wave equation with memory, Boll. Un. Mat.Ital. B (7) 8 (1994), no. 2, 289-303.

University 20 Aout 1955- Skikda, Algeria, [email protected]


11 Moore-Penrose Inverse and Partial IsometriesSafa Menkad

In this talk, we shall give a characterization of the class of all normal partial isometries, using a versionof Corach-Porta-Recht inequality for Moore-Penrose invertible operators.

References

[1] G. Corach, R. Porta, and L. Recht, An operator inequality, Linear Algebra Appl. 142(1990), 153-158,

[2] R. Hart and M. Mbekhta, on generalized inverse in C∗ -algebra, Studia mathematica, 103 (1992) ,71-77

[3] S. Menkad and A Seddik, operator inequalities and normal operators, Banach J. Math. Ana.,6 (2012),187-193. Cremona, Algorithms for Modular Elliptic Curves, 2nd Edition, Cambridge Univ. Press,Cambridge, 1997,

[4] A. Seddik, Some results related to Corach-Porta-Recht inequality, Proc. Amer. Math. Soc. 129(2001),3009-3015.

Department of Mathematics, Faculty of Science, Hadj Lakhdar University, Batna, Algeria, menkad [email protected]


12 Multiplicity Result for the Hamiltonian SystemTacksunJung and Q-Heung Choi

We get a theorem which shows the multiple weak solutions for the bifurcation problem of the su-perquadratic nonlinear Hamiltonian system. We obtain this result by using the variational method, thecritical point theory in terms of the S1-invariant functions and the S1-invariant linear subspaces.

References

[1] K. C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhauser, (1993),

[2] M. Degiovanni, L. Olian Fannio, Multiple periodic solutions of asymptotically linear Hamiltoniansystems, Quaderni Sem. Mat.Brescia 8/93, (1993),

[3] T. Jung, Q. H. Choi, On the number of the periodic solutions of the nonlinear Hamiltonian system,Nonlinear Analysis TMA, 71, No. 12 e1100-e1108 (2009),

[4] T. Jung, Q. H. Choi, Periodic solutions for the nonlinear Hamiltonian systems, Korean Journal ofMathematics 17, No. 3 331-340 (2009),

[5] T. Jung, Q. H. Choi, Existence of four solutions of the nonlinear Hamiltonian system with nonlinearitycrossing two eigenvalues, Boundary Value Problems, 2008, 1-17.

Kunsan National University, Department of Mathematics, Kunsan 573-701, Republic of Korea, tsjung @kunsan.ac.kr

Q- Heung Choi: Inha University, Department of Mathematics Education, Incheon 402-751, Republic of Korea, [email protected]

This work(Tacksun Jung) was supported by Basic Science Research Program through the National Research Foundationof Korea(NRF) funded by the Ministry of Education, Science and Technology (KRF-2010-0023985).


13 One-Parameter Apostol-Bernoulli Polynomials and Apostol-Euler PolynomialsVeli Kurt

In this work, we define one-parameter Apostol-Bernoulli polynomials B(β)n (x;α, λ) of order β and one-

parameter Apostol-Euleri polynomials E(β)n (x;α, λ) of order β, β ∈ N. We prove some identities and

relations between these polynomials. Also, we give different form analogue of the Srivastava-Pinteradditional theorem for these polynomials.

References

[1] T. M. Apostol, On the Lerch zeta function, Pasific J. Math., 1 (1951), 161-167.

[2] J. Choi, P. J. Aderson and H. M. Srivastava, Some q-extensions of the Apostol-Bernoulli and Apostol-Euler polynomials of order n and the multiple Hurwitz zeta functions, Appl. Math. and Comp., 199(2008), 723-737.

[3] M. Garg, K. Jain and H. M. Srivastava, Some relationships between the generalized Apostol-Bernoullipolynomials and Hurwitz-Lerch zeta functions, Integral Trans. and Special Function, 17 (2007), 803-815.

[4] B.-N. Guo and F.Qi, Some identities and an explicit formula for Bernoulli and Stirling numbers, J.of Comp. and Appl. Math., 255 (2014), 568-579.

[5] D. S. Kim and T. Kim, A study on the integral of the product of several Bernoulli polynomials,Rocky Mountain J. Math., (2014), (Submitted).

[6] D.-Q. Lu and H. M. Srivastava, Some series identities involving the generalized Apostol type andrelated polynomials, Comp. and Math. with Appl., 62 (2011), 3591-3602.

[7] Q.-M Luo, Multiplication formulas for Apostol-type polynomials and Multiple Alternating sums,Mathematical Notes, 91 (2012), 46-57.

[8] Q.-M Luo and H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Eulerpolynomials, J. Math. Analy. Appl., 308 (2005), 290-302.

[9] Q.-M Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Eulerpolynomials, Computers and MAth. with Appl., 51 (2006), 631-642.

[10] Q.-M Luo, B. Guo, F. Qi and L. Debnath, Generalizations of Bernoulli numbers and polynomials,Int. J. Math. and Math. Sciences, 59 (2003), 3769-3776.

[11] F. Qi, Explicit formulas for computing Euler polynomials in terms of the second kind Stirling number,arXiv: 1310.592[v], 19 oct 2013.

[12] H. M. Srivastava and J. Choi, Series associated with the zeta and related functions, Kluwer AcademicPublishers, London 2001.

[13] H. M. Srivastava and A. Pinter, A remarks on some relationships between the Bernoulli and Eulerpolynomials, Appl. Math. Letters, 17 (2004), 375-380.

Department of Mathematics, Faculty of Sciences, University of Akdeniz, TR-07058 Antalya, Turkey, [email protected]


14 On p-Bernoulli NumbersMourad Rahmani

In this talk, we define a new family of p-Bernoulli numbers which are derived from the Gaussian hyper-geometric function, and we establish some basic properties. Furthermore, an algorithm for computingBernoulli numbers based on three-term recurrence relation is given. A similar algorithm for Bernoullipolynomials is also presented.

References

[1] S. Akiyama, Y. Tanigawa, Multiple zeta values at non-positive integers, Ramanujan J., 5 (4) (2001)327–351.

[2] A. Z. Broder, The r-Stirling numbers, Discrete Math., 49 (3) (1984) 241–259.

[3] K.-W. Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Seq., 4 (1) (2001)Article 01.1.6.

[4] D. Dumont, Matrices d’Euler-Seidel, Semin. Lothar. Comb. 5, B05c (1981), 25 p.

[5] M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Seq., 3 (2000) Article00.2.9.

[6] D. E. Knuth, T. J. Buckholtz, Computation of tangent, Euler, and Bernoulli numbers. Math. Comp.21 (1967), 663–688.

[7] M. Rahmani, The Akiyama–Tanigawa matrix and related combinatorial identities, Linear AlgebraAppl., 438 (2013), pp. 219–230.

[8] M. Rahmani, Generalized Stirling transform, preprint, (2012), available electronically athttp://arxiv.org/abs/1212.0957.

USTHB, Faculty of Mathematics, P. O. Box 32, El Alia, Bab Ezzouar, 16111, Algiers, Algeria, [email protected]


15 The Roots of a Dual Split QuaternionHesna Kabadayı

In this paper, we express De Moivre’s formula for dual split quaternions and find roots of a dual splitquaternion using this formula.

References

[1] R. Ablamowicz and G. Sobczyky, “Lectures on clifford (Geometric) Algebras and Applications”Birkhauser, Boston 2004.

[2] L. Brand,. The Roots of a Quaternion, American Mathematical Monthly 49 (8) (1942) 519-520.

[3] E. Cho,. De Moivre’s Formula for Quaternions, Applied Mathematics Letters 11(6) (1998) 33-39.

[4] W. K. Clifford Preliminary sketch of bi-quaternions, Proc. of London Math. Soc. 4 n. 64, 65 (1873),361–395

[5] H. Kabadayi. and Y. Yayli. De Moivre’s formula for Dual Quaternions, Kuwait journal of Scienceand Engineering, 38 (1A) pp. 15-23, 2011.

[6] S. Li - Q. J. Ge, Rational Bezier Line Symmetric Motions, ASME J. of Mechanical Design, 127 (2)(2005), 222–226.

[7] C. Mladenova, “Robot problems over configurational manifold of vector-parameters and dual vector-parametes” J. Intelligent and Robotic systems 11 (1994) 117-133.

[8] I. Niven, The Roots of a Quaternion, American Mathematical Monthly 49 (6) (1942) 386-388.

[9] M. Ozdemir,. Roots of a Split Quaternion, Applied mathematics letters 22(2009) 258-263

[10] E. Study, Geometrie der Dynamen, Leipzig, 1903.

[11] R. Wald, Class. Quant. Gravit. 4, 1279, 1987.

Ankara University, Science Faculty, Mathematics Department, Tandogan, Ankara-Turkiye, [email protected], [email protected]


16 On Some Inequalities for Hadamard Product of Special Typesof MatricesSeyda Ildan and Hasan Kose

In this paper, we review some determinantal inequalities for Hadamard product of positive definitematrices, M−matrices and inverse M−matrices. Than we improve these inequalities for some specialtypes of matrices.

References

[1] S. Chen, Inequalities for M−matrices and inverse M−matrices, Linear Algebra and Its Applications,426(2007) 610-618.

[2] J. Liu,L. Zhu, Some Improvement Of Oppenheim’s Inequality For M−Matrices, SIAM J. MATRIXANAL., APPL., Vol. 18, No. 2, pp.305-311.

[3] B.-Y. Wang, X. Zhang, F. Zhang, On The Hadamard Product Of Inverse M−Matrices, Linear Algebraand Its Applications, 305(2000) 23-31.

[4] S. Chen, Some determinantal Inequalities for Hadamard Product of Matrices, Linear Algebra and ItsApplıcations, 368(2003) 99-106.

[5] K. Fan, Inequalities for M−matrices, Indag. Math., 26 (1964), pp. 602-610.

[6] T. Ando, Inequalities for M−matrices, Linear and Multilinear Algebra, 8 (1980), pp. 291-316.

[7] R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, 1.

Selcuk University, Konya, Turkey, [email protected]


17 Generalized Newton Transformation and its Application toTransversal SubmanifoldsAbdelmalek Mohammed

In this paper, we study some properties of generalized Newton transformation TU of a family of endo-morphisms. As application we establish a relation between the transversality of two submanifolds andellipticity of TU .

References

[1] M. P. do Carmo, Riemannian Geometry, Birkhauser, 1979 first edition.

[2] K. Andrzejeweski, The Newton transformation and new integral formulae for foliated manifolds, AnnGlob Anal Geom, 37 (2010), 103-111.

[3] L. J. Alias, J. H. S. De Lira, J. M. Malacarne. Constant higher order mean curvature hypersurfacesin Riemannian spaces, J. Inst. Math. Jussieu 5 (2006), no, 4, 527-562.

[4] W. Kozlowski, Generalized Newton transformation and its applications to extrinsic geometry, preprint.

Ecole preparatoire en sciences economiques, commerciales et sciences de gestion, Departement de mathematiques,Tlemcen -Algerie, [email protected]


18 Multiple Positive Solutions for Elliptic Singular Systems withHardy Sobolev ExponentsBenmansour Safia

In this work, we prove the existence of at least two positive solutions for an elliptic singular system of twoweakly coupled equations with singular weights and critical Hardy Sobolev exponents. We use MountainPass theorem and Eukland’s variationnal principle.

References

[1] M. Bouchekif, A. Matallah, On singular elliptic equations involving a concave term and criticalCafarelli-Kohn-Nirenberg exponent. Math. Nachr. 284, 177-185 (2011).

[2] H. Brezis, E. Lieb, A relation between pointwise convergence of functions and convergence of functionals , Proc . Amer. Math . Soc . 88 , 486 -490 (1983 ).

[3] L. Cafarelli, R. Kohn, L. Nirenberg, First order interpolation inequality with weights, Compos. Math.53, 259-275 (1984).

[4] F. Catrina, Z. Wang, On the Cafarelli-Kohn -Nirenberg inequalities: sharp constants, existence (andnon existence) and symmetry of extremal func tions , C omm . Pure Appl. Math . 54 , 229 -257 (2001).

[5] J. Chen , Multiple positive solutions for a class of non linear elliptic equations, J. Math. Anal. Appl.295, 341-354 (2004 ).

[6] J. Chen, E. M. Rocha, Four solutions of an inhomogeneous elliptic equation with critical exponentand singulareties, Non linear Anal. 71, 4739- 4750 (2009 ).

[7] K.S. Chou, C.W. Chu, On the best constant for a weighted Sobolev-Hardy Inequality J. London Math.Soc. 2, 137 -151(1993).

Ecole preparatoire en sciences economiques, commerciales et sciences de gestion, Departement de mathematiques,Tlemcen-Algerie, [email protected]


19 A Collocation Method for Solution of the Nonlinear Lane-Emden type Equations in Terms of Generalized BernsteinPolynomialsAysegul Akyuz-Dascıoglu and Nese Isler Acar

In this talk, a collocation method based on Bernstein polynomials defined on the interval [a, b] ispresented for approximate solution of the nonlinear Lane-Emden type equations that have an importantplace in astrophysics and mathematical physics. The proposed method reduces the solution of nonlinearproblem to the solution of a system of linear algebraic equations iteratively by using quasilinearizationtechnique and collocation points. Some numerical examples are given to illustrate the efficiency, validityand applicability of the method.

References

[1] C. M. Bender, K. A. Milton, S. S. Pinsky and L. M. Simmons, A new perturbation approach tononlinear problems, J. Math. Phys. 30 (1989) 1447-1455.

[2] A. M. Wazwaz, A new algorithm for solving differential equations of Lane-Emden type, Appl. Math.Comput. 118 (2001) 287-310.

[3] A. M. Wazwaz, A new method for solving singular value problems in the second order ordinarydifferential equations, Appl. Math. Comput. 128 (2001) 45-57.

[4] J. I. Ramos, techniques for singular initial-value problems of ordinary differential equations, Appl.Math. Comput. 161 (2005) 525–542.

[5] H. Aminikhah, S. Moradian, Numerical Solution of Singular Lane-Emden Equation, Math. Phys.doi:10.1155/2013/507145.

[6] A. Yıldırım, T. Ozis, Solutions of singular IVPs of Lane-Emden type by homotopy perturbationmethod, Phys. Lett. A 369 (2007) 70-76.

[7] M. S. H. Chowdhury, I. Hashim, Solutions of a class of singular second-order IVPs by homotopy-perturbation method, Phys. Lett. A. 368 (2007) 305-313.

[8] G. Hojjeti, K. Parand, An efficient computational algorithm for solving the nonlinear Lane-Emdentype equations, World Academy of Science, Engineering and Technology, 56 (2011) 1521-1526.

[9] R. K. Pandey, N. Kumar, Solution of Lane–Emden type equations using Bernstein operational matrixof differentiation, New Astron. 17 (2012) 303–308.

[10] D. G. Wang, W. Y. Song, P. Shi and H. R. Karimi, Approximate Analytic and Numerical Solutionsto Lane-Emden Equation via Fuzzy Modeling Method, Math. Probl. Eng. doi:10.1155/2012/ 259494.

[11] K. Parand, M. Dehghan, A. R. Rezaei and S. M. Ghaderi, An approximation algorithm for thesolution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functionscollocation method, Comput. Phys. Commun. 181 (2010) 1096–1108.

Aysegul Akyuz-Dascıoglu: Pamukkale University, Faculty of Arts&Sciences, Department of Mathematics, Kınıklı,Denizli-Turkey, [email protected]

Nese Isler Acar: Mehmet Akif Ersoy University, Faculty of Arts&Sciences, Department of Mathematics, Istiklal, Burdur-Turkey, [email protected]

This work is supported by Scientific Research Project coordination Unit of Pamukkale University, No:2012FBE036.


20 GALA and GADP2 Comparison for the Scheduling Problemof Rm/Sijk/Cmax

Duygu Yilmaz Eroglu and H.Cenk Ozmutlu

We presented GALA, which is hybrid local search algorithm for the scheduling problem with setup timesthat includes non-identical parallel machines. This problem type is studied by many of researcher andmost of them compare their algorithms via datasets from literature. In this study, we will compare ourstudy’s results with GADP2 (integrating the dominance properties with a genetic algorithm which isproposed by Chang and Chen (2011)) algorithm’s results using the same datasets. In spite of GALA’slocal search is inspired from dominant properties method of GADP2, the results of GALA gives betterresult. This is probably caused by chromosome structure of GALA which is constituted by randomnumbers that are generated between 0 and 1.

References

[1] Arnaout, J.P., Rabadi, G., & Musa, R. (2010) A two-stage Ant Colony Optimization algorithm tominimize the makespan on unrelated parallel machines with sequence-dependent setup times. Journalof Intelligent Manufacturing, 21, 693-701.

[2] Chang, P.C., & Chen, S.H. (2011). Integrating dominance properties with genetic algorithms forparallel machine scheduling problems with setup times. Applied Soft Computing, 11, 1263–1274.

[3] Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading.

[4] Rabadi, G., Moraga, R., & Al-Salem, A. (2006). Heuristics for the Unrelated Parallel Machine Schedul-ing Problem with Setup Times. Journal of Intelligent Manufacturing, 17, 85–97.

[5] Vallada, E., & Ruiz, R. (2011). A genetic algorithm for the unrelated parallel machine schedulingproblem with sequence dependent setup times. European Journal of Operational Research, 211, 612–622.

[6] SchedulingResearch. (2005). Accessed June 07, 2012 from http://SchedulingResearch.com

Duygu Yilmaz Eroglu (Corresponding Author): Department of Industrial Engineering, Uludag University, GorukleCampus, Bursa 16059, Turkey, [email protected]

H.Cenk Ozmutlu: Department of Industrial Engineering, Uludag University, Gorukle Campus, Bursa 16059, Turkey


21 Improved MIP Model for Parallel Machines’ Scheduling Prob-lemDuygu Yilmaz Eroglu and H.Cenk Ozmutlu

In this study, MIP model, which is developed for unrelated parallel machines, is improved and additionalconstraints that satisfies equal sub orders are added into the formulation. This research is motivated bya practical need at a loom scheduling. MIP helps us in this problem to validate the developed heuristicsmethods, using small scale data sets from literature. The comparison of the results of developed MIPmodel and heuristic algorithm shows effectiveness of presented algorithms. Job splitting is scarcely studiedin the literature but needs more attention because of possible flexibility effects also on the other sectors(i.e logistics) besides scheduling.

References

[1] Ruiz, R., Maroto, C. (2006). A genetic algorithm for hybrid flowshops with sequence dependent setuptimes and machine eligibility. European Journal of Operational Research, 169, 781–800.

[2] Ruiz, R., Serifoglu, F.S., Urlings, T. (2008). Modeling realistic hybrid flexible flowshop schedulingproblems. Computers & Operations Research, 35, 1151-1175.

[3] Lin, Y., Li, W. (2004). Parallel machine scheduling of machine-dependent jobs with unit-length.European Journal of Operational Research, 156, 261-266.

[4] Liao, L.W., Sheen, G.J. (2008). Parallel machine scheduling with machine availability and eligibilityconstraints. European Journal of Operational Research, 184 458-467.

[5] Centeno, G., Armacost, R.L. (2004). Minimizing makespan on parallel machines with release timeand machine eligibility restrictions. International Journal of Production Research, 42, 6, 1243-1256.

Duygu Yilmaz Eroglu (Corresponding Author): Department of Industrial Engineering, Uludag University, GorukleCampus, Bursa 16059, Turkey, [email protected]

H.Cenk Ozmutlu: Department of Industrial Engineering, Uludag University, Gorukle Campus, Bursa 16059, Turkey


22 Multiple Positive Solutions for Elliptic Singular Systems withCafarelli Kohn Niremberg ExponentsMatallah Atika

In this work, we prove the existence of at least two positive solutions for an elliptic singular system oftwo weakly coupled equations with singular weights and critical Cafarelli Kohn Niremberg exponents.We use Mountain Pass theorem and Eukland’s variationnal principle.

References

[1] H. Brezis, E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88, 486 -490 (1983).

[2] L. Cafarelli, R. Kohn, L. Nirenberg, First order interpolation inequality with weights, Compos. Math.53, 259-275 (1984).

[3] F. Catrina, Z. Wang, On the Cafarelli-Kohn -Nirenberg inequalities: sharp constants, existence (andnon existence), and symmetry of extremal func tions, Comm. Pure Appl. Math. 54, 229 -257 (2001).

[4] J. Chen , Multiple positive solutions for a class of non linear elliptic equations, J. Math. Anal. Appl.295, 341-354 (2004).

[5] J. Chen, E. M. Rocha, Four solutions of an inhomogeneous elliptic equation with critical exponentand singulareties, Non linear Anal. 71, 4739- 4750 (2009).

[6] K.S. Chou, C.W. Chu, On the best constant for a weighted Sobolev-Hardy Inequality J. London Math.Soc. 2, 137 -151(1993).

Ecole preparatoire en sciences economiques, commerciales et sciences de gestion, Departement de mathematiques,Tlemcen-Algerie, atika [email protected]


23 Positive Solution for a Singular Second-Order Discrete Three-Point Boundary Value ProblemNoor Halimatus Sa’diah Ismail and Mesliza Mohamed

Using the Krasnoselskii fixed point theorem, we prove the existence and multiplicity of positive solutionfor a singular three point boundary value problem

∆2y(k − 1) + λh(k)f(y(k)) = 0, k ∈ 1, ..., T,

y(0)− α∆y(0), y(T + 1) = βy(n).

where f is singular at y = 0, λ > 0 and T ≥ 3 is a fixed positive integer, n ∈ 2, ..., T − 1, constantα, β > 0 such that H := T + 1− βn+ α(1− β) > 0, and T + 1− βn > 0.

References

[1] X. Lin and W. Liu, Three positive solutions for a second order diference equation with three-pointboundary value problem, J. Appl. Math. Comput., 31 (2009), 279-288.

[2] M. Krasnoselskii, Positive solutions of operator equations, Noordhoff, Groningen, 1964.

[3] M. Mohamed and O. Omar, Positive periodic solutions of singular first order functional differenceequation, Int. J. of Math Analysis., vol 6, 54(2012), 2665-2675.

[4] F. M. Atici and A. Cabada, Existence and uniqueness result for the second-order periodic boundaryvalue problems, Comp. Math. Appl., 45(2003), 1417-1427.

[5] W. A. W. Azmi, M. Mohamed, Existence and multiplicity of positive solutions for singular secondorder Dirichlet boundary value problem, Proceedings of the International Conference on MathematicalSciences and Statistics (ICMSS2013) 2013, Vol 1557, Isue 1, 66–71, AIP Publishing.

Noor Halimatus Sa’diah Ismail: Fakulti Sains Komputer & Matematik, Universiti Teknologi MARA (Pahang), 26400Bandar Tun Abdul Razak, Jengka, Malaysia., [email protected]

Mesliza Mohamed (Corresponding author): Fakulti Sains Komputer & Matematik, Universiti Teknologi MARA (Pa-hang), 26400 Bandar Tun Abdul Razak, Jengka, Malaysia, [email protected]

The authors thank to Ministry of Higher Education for Fundamental Research of Grant Sciences (600-RMI/FRGS5/3/Fst(9/2012))


24 Positive Solution to Fourth Order Three-Point BoundaryValue ProblemM.Mohamed, M.S.M.Noorani, M.S.Jusoh, M.N.M.Fadzil and R.Sa-

ian

This work concerned with the fourth order boundary value problem u4(t) + f(t, u(t), u′(t)) = 0,0 < t < 1, subject to boundary conditions u(0) = u′(0) = u′′(0) = 0 and u′′(1) − αu′′(η) = λ where0 < η < 1 and α ∈ [0, 1

η ] are constant and λ ∈ [0,+∞) is a parameter. By imposing a sufficient structure

on the nonlinearity f(t, u, u′), we deduce the existence of at least one positive solution to the problem byapplying the Krasnosel’skii fixed point theorem.

References

[1] R. Ma, J. Zhang, S. Fu, The method of upper and lower solutions for fourth-order two point boundaryvalue problems, J. Math. Anal. Appl, (1997), 215, 415–422.

[2] R. Ma, H. Wang, On The Existence Of Positive Solutions Of Fourth-Order Ordinary DifferentialEquation, Appl. Anal, (1995), 59, 225–231.

[3] Q. Yao, Existence And Multiplicity Of Positive Solutions To A Class Of Nonlinear Cantilever BeamEquations, J. Syst. Sci. Math. Sci, (2009), 1, 63–69.

[4] Z. Bai, H. Wang, On The Positive Solutions Of Some Nonlinear Fourth-Order Beam Equations, J.Math. Anal. Appl, (2002), 270, 357–368.

[5] JR. Graef, C. Qian, B. Yang, A Three Point Boundary Value Problem For Nonlinear Fourth-OrderDifferential Equations, J. Math. Anal. Appl, (2003), 287, 217–233.

[6] Y. Sun and C Zhu, Existence of positive solutions for singular fourth order three-point boundary valueproblems, Advances in Difference Equations, (2013) 2013:51, pp 13.

M. Mohamed (Corresponding author), Fakulti Sains Komputer & Matematik, Universiti Teknologi MARA (Pahang),26400 Bandar Tun Abdul Razak, Jengka, Pahang, Malaysia, [email protected]

M. S. M. Noorani: Faculty of Science & Technology, School of Mathematical Sciences, Universiti Kebangsaan Malaysia,[email protected]

M. S. Jusoh, Faculty of Civil Engineering, Universiti Teknologi MARA (Pahang), 26400 Bandar Tun Abdul Razak,Jengka, Pahang, Malaysia, [email protected]

M. N. M. Fadzil, Fakulti Sains Komputer & Matematik, Universiti Teknologi MARA (Perlis), 02600 Arau, Perlis,Malaysia, [email protected]

R. Saian:Fakulti Sains Komputer & Matematik, Universiti Teknologi MARA (Perlis), 02600 Arau, Perlis, Malaysia,[email protected]

The authors thank to Ministry of Higher Education for Fundamental Research of Grant Sciences (600-RMI/FRGS5/3/Fst(9/2012))


25 Existence of Positive Solutions for Non-Homogeneous BVPsof p-Laplacian Difference EquationsFatma Tokmak and Ilkay Yaslan Karaca

In this talk, by using Avery-Peterson fixed point theorem, we investigate the existence of at least threepositive solutions for a third order p-Laplacian difference equation. As an application, an example isgiven to illustrate our main results.

References

[1] D. R. Anderson, Discrete third-order three-point right-focal boundary value problems, Comput. Math.Appl., 45 (2003), 861-871,

[2] R. Avery and A. Peterson, Three positive fixed points of nonlinear operators on an ordered Banachspace, Comput Math Appl., 208 (2001), 313-322,

[3] Z. He, On the existence of positive solutions of p-Laplacian difference equations, J. Comput. Appl.Math., 161 (2003), 193-201,

[4] I. Y. Karaca, Discrete third-order three-point boundary value problem, J. Comput. Appl. Math., 205(2007), 458-468,

[5] Y. Liu, Studies on nonhomogeneous multi-point BVPs of difference equations with one-dimensionalp-Laplacian, Mediterr. J. Math., 8 (2011), 577-602,

[6] Y. Liu, Three positive solutions of multi-point BVPs for difference equations with the nonlinearitydepending on ∆-operator, An. Stiint. Univ. ”Ovidius” Constanta Ser. Mat., 20 (2012), 65-81,

[7] J. Xia, L. Debnath, H. Jiang and Y. Liu, Three positive solutions of Sturm-Liouville type multi-pointBVPs for second order p-Laplacian difference equations, Bull. Pure Appl. Math., 4 (2010), 266-287.

Fatma Tokmak: Gazi University, Faculty of Science, Department of Mathematics, 06500 Teknikokullar, Ankara-Turkeyand Ege University, Faculty of Science, Department of Mathematics, 35100 Bornova, Izmir-Turkey, [email protected] [email protected]

Ilkay Yaslan Karaca: Ege University, Faculty of Science, Department of Mathematics, 35100 Bornova, Izmir-Turkey,[email protected]


26 L2 Norm Deconvolution Algorithm Applied to UltrasonicPhased Array Signal ProcessingAbdessalem Benammar, Redouane Drai and Ahmed Khechida

Detection of failure in laminate composites is complicated compared with ordinary non-destructive testingfor metal materials as they are sensitive to echoes drown in noise due to the properties of the constituentmaterials and the multi-layered structure of the composites. In recent years, rapid development in thefields of microelectronics and computer engineering lead to wide application of phased array systems.Different signal processing and image reconstruction techniques are applied in ultrasonic testing. In thiswork, the objective is to improve the time resolution of signals obtained from inspection of CFRP sample.The signal processing scheme used is based on L2 Norm deconvolution of the measured signal by fastsequential algorithm. This algorithm performs a search of events by increasing order of importance withrespect to a criterion which is described in detail. It gives good results over a wide range of applications.The experimental results show that the L2 Norm deconvolution can enhance the time resolution of theCFRP ultrasonic phased array inspection effectively and help identify the location of defects. Keywords:Ultrasonic Phased Array, signal processing, L2 Norm deconvolution.

References

[1] Reza Bohlouli, Babak Rostami, and Jafar Keighobadi, Application of Neuro-Wavelet Algorithm inUltrasonic-Phased Array Nondestructive Testing of Polyethylene Pipelines, Journal of Control Scienceand Engineering, (2012),

[2] S.C. Ng, N. Ismail, Aidy Ali, Barkawi Sahari, J.M. Yusof, B.W. Chu. Non-destructive Inspection ofMulti-layered Composites Using Ultrasonic Signal Processing, Materials Science and Engineering 17(2011),

[3] Zhang Yicheng, Li Xiaohong, Zhang Jun, Ding Hui, Model based reliability analysis of PA ultrasonictesting for weld of hydro turbine runner, Procedia Engineering 16 (2011) 832–839,

[4] R. J. Ditchburn and M. E. Ibrahim, Ultrasonic Phased Arrays for the Inspection of Thick-SectionWeldsa, DSTO Defence Science and Technology Organisation 506 Lorimer St Fishermans Bend Vic-toria 3207 Australia,

Abdessalem Benammar: Welding and NDT Research Center (CSC), BP 64, Cheraga, Algeria, Abs [email protected] Drai: Welding and NDT Research Center (CSC), BP 64, Cheraga, Algeria.Ahmed Khechida: Welding and NDT Research Center (CSC), BP 64, Cheraga, Algeria.


27 Multi-Soliton Solutions for Non-Integrable Equations: Asymp-totic ApproachGeorgy A.Omel’yanov

We describe an approach to construct multi-soliton asymptotic solutions for essentially non-integrableequations. The general idea is realized for the GKdV-4 equation:

∂u

∂t+∂u4

∂x+ ε2 ∂

3u

∂x3= 0, x ∈ R1, t > 0,

where the dispersion parameter ε is assumed to be small.It has been proved that two and three solitons interact preserving in the leading term the KdV-type

scenario of collision: they pass through each other almost without deformation. At the same time, asmall radiation tail appears on the left of the solitons.

Our main tool is the Weak Asymptotics Method [1, 2]. We indicate also how to modify this approachin order to construct N -soliton asymptotic solutions for N ≥ 3. A brief review of asymptotic methods aswell as results of numerical simulation are included.

References

[1] V. G. Danilov, G. A. Omel’yanov, Weak asymptotics method and the interaction of infinitely narrowdelta-solitons, Nonlinear Analysis: Theory, Methods and Applications, 54 (2003), 773–799

[2] V. G. Danilov, G. A. Omel’yanov, V. M. Shelkovich, Weak asymptotics method and interaction ofnonlinear waves, in: M.V. Karasev (Ed.), Asymptotic methods for wave and quantum problems, AMSTrans., Ser. 2, 208, AMS, Providence, RI, 2003, 33–164

Universidad de Sonora, Departamento de Matematicas, calle Rosales y Blvd. Encinas, s/n, 83000, Hermosillo, Sonora,Mexico, [email protected]

This work was supported by the SEP-CONACYT under grant 178690 (Mexico)


28 On Interpolation Functions for the q-analogue of the EulerianNumbers Associated with any CharacterMustafa Alkan and Yilmaz Simsek

Simsek [1] defined generating functions for the Eulerian numbers and polynomials. In this paper, we studyon these generating functions and their properties. The aim of this paper is to construct q-interpolationfunctions of the generalized Eulerian type numbers attached to any characters. We give some results,remarks and identities related to these functions and characters.

References

[1] Y. Simsek, interpolation function of the Eulerian type polynomils and numbers, Adv. Studies Con-temp. Math 23 (2013)2, 301-307.

[2] M. Alkan and Y. Simsek, Generating function for q-Eulerian polynomials and their decompositionand applications, Fixed Point Theory Appl. 2013, 72.

[3] Y. Simsek, On q-analogue of the twisted L-functions and q-twisted Bernoulli numbers, J. KoreanMath. Soc. 40(6) (2003), 963-975.

[4] 78. Y. Simsek, Generating Functions for q-Apostol Type Frobenius-Euler Numbers and Polynomials,Axioms 1(2012) 395-403.

[5] J. Choi P. J. Anderson and H. M. Srivastava, Some q -extensions of the Apostol-Bernoulli and theApostol-Euler polynomials of order n, and the multiple Hurwitz zeta function, Appl. Math. Com-put. 2008, 199:723-737. Y. Simsek, On q-analogue of the twisted L-functions and q-twisted Bernoullinumbers, J. Korean Math. Soc. 40(6) (2003), 963-975.

[6] H. M. Srivastava, T. Kim and Y. Simsek, q-Bernoulli numbers and polynomials associated withmultiple q-zeta functions and basic L-series, Russian J. Math Phys. 2005, 12:241-268.

Mustafa Alkan: University of Akdeniz, Faculty of Science, Department of Mathematics, TR-07058 Antalya, Turkey,[email protected]

Yilmaz Simsek: University of Akdeniz, Faculty of Science, Department of Mathematics, TR-07058 Antalya, Turkey,[email protected]


29 Computation of p-values for Mixtures of GaussiansBurcin Simsek and Satish Iyengar

For unimodal distributions, p-values are typically tail probabilities. In this paper, we address the problemof computing p-values for mixtures of the Gaussian distributions. The “tail’ regions are those that havesmall probability under each component of the mixture. We compare the use of moment methods andexponential tilting to estimate the probabilities of such tail regions.

Burcin Simsek: Statistics Department University of Pittsburgh, Pittsburgh, PA-USA, [email protected]; burcinsim @gmail.com

Satish Iyengar: Statistics Department University of Pittsburgh, Pittsburgh, PA-USA, [email protected]


30 Nonclassical Appell PolynomialsRahime Dere and Yilmaz Simsek

In this paper we study on the nonclassical Appell polynomials associated with umbral calculus. Weintroduce nonclassical Bernoulli polynomials and nonclassical Euler polynomials, which are the Appellpolynomials. Furthermore, we give some identities of these polynomials by using nonclassical umbralcalculus methods.

References

[1] R. Dere and Y. Simsek, Genocchi polynomials associated with the Umbral algebra, Appl. Math.Comput. 218(3) (2011) 756-761.

[2] R. Dere and Y. Simsek, Applications of umbral algebra to some special polynomials, Adv. StudiesContemp. Math. 22 (2012) 433-438.

[3] R. Dere and Y. Simsek, Remarks on the Frobenius-Euler Polynomials on the Umbral Algebra, Nu-merical Analysis and Applied Mathematics ICNAAM 2012: International Conference of NumericalAnalysis and Applied Mathematics. AIP Conference Proceedings. 1479 (2012), 348-351.

[4] R. Dere and Y. Simsek, Normalized polynomials and their multiplication formulas, Advances in Dif-ference Equations. (2013), 2013:31.

[5] R. Dere, Y. Simsek and H. M. Srivastava, A unified presentation of three families of generalizedApostol type polynomials based upon the theory of the umbral calculus and the umbral algebra,Journal of Number Theory 133 (2013), 3245-3263.

[6] E. C. Ihrig and M. E. H. Ismail, A q-umbral calculus, J. Math. Anal. Appl. 84 (1981) 178-207.

[7] V. Kac and P. Cheung, Quantum Calculus, Springer, 2002.

[8] S. Roman, More on the Umbral Calculus, with Emphasis on the q-Umbral Calculus, J. Math. Anal.Appl. 107(1) (1985) 222-254.

[9] S. Roman, The Umbral Calculus, Dover Publ. Inc. New York, 2005.

Rahime Dere: University of Akdeniz, Faculty of Science, Department of Mathematics, TR-07058 Antalya, Turkey,[email protected]

Yilmaz Simsek: University of Akdeniz, Faculty of Science, Department of Mathematics, TR-07058 Antalya, Turkey,[email protected]


31 Remarks on the Central Factorial NumbersYilmaz Simsek

In [3], we gave some analytic functions which are related to the generating functions for the centralfactorial numbers. By using these functions, we derive identities-some old and some new-for the centralfactorial numbers, the Stirling numbers and special numbers.

References

[1] J. Cigler, Fibonacci Polynomials and Central Factorial Numbers, Preprint.

[2] S. Roman, The Umbral Calculus, Dover Publ. Inc. New York, 2005.

[3] Y. Simsek, Special Numbers on Analytic Functions, Applied Mathematics 2014.

[4] Y. Simsek, On q-Deformed Stirling numbers, International Journal of Computer Mathematics, 15,70-80; 2010.

[5] Y. Simsek, Generating Functions for Generalized Stirling type Numbers, Array Type Polynomials,Eulerian Type Polynomials and Their Applications, Fixed Point Theory and Applications, 87, 343-1355; 2013.

[6] H. M. Srivastava and G.-D. Liu, Some Identities and Congruences Involving a Certain Family ofNumbers, Russian Journal of Mathematical Physics, 16, 536-542; 2009.

University of Akdeniz, Faculty of Science, Department of Mathematics, TR-07058 Antalya, Turkey, [email protected]


32 Nodals Solutions of the Fourth Order Equations InvolvingPaneitz-Branson Operator with Critical Sobolev ExponentBoughazi Hichem

Given (M, g) a smooth compact Einstein manifold of dimension n ≥ 5, with negative scalar curva-ture Sg, for u ∈ C∞(M), the geometric Paneitz-Branson operator Pg is reduced to Pgu = ∆2

gu +anSg∆gu+ bnS

2gu.M.Benalili and H.Boughazi defined the k−th Paneitz-Branson invariant by µk(M, g) =

infg∈[g]

λk(g)[vol(M, g)]4n , where the λk(g) is the k−th eigenvalue when the scalar curvature Sg is negative,

the Paneitz-Branson operator is non necessary coercive and we give a new technic for study the standardPaneitz-Branson invariant µ(M, g), the first Paneitz-Branson invariant µ1(M, g) and the second Paneitz-Branson invariant µ2(M, g). The main point of this work is to complete the results of [1] M.Benalili,H.Boughazi. We recall that study the standard Paneitz-Branson invariant is a challenging open prob-lem, we find nodals solutions in few cas, study the positivite of solutions it seem to be impossible, wehave always µ(M, g) > −∞ contrary to µ1(M, g) and µ(M, g) is always attained, the nodals solutionsw of the fourth order equations involving Paneitz-Branson operator with critical Sobolev exponent i.e,Pgv = µ2(M, g)|w|N−2w.

References

[1] M.Benalili, H.Boughazi. Nodals solutions of the fourth order equations involving Paneitz-Bransonoperator with critical Sobolev exponent (submit).

[2] M.Benalili, H.Boughazi. On the second Paneitz Branson invariant , Houston J. Math. 36 (2010),no.2, 393–420. MR 2661253 (2011h:58047)

[3] M.Benalili, H.Boughazi. The second Yamabe invariant with singularities, Annales mathematiqueBlaise Pascal.Volume 19, no.1, (2012),p.147-176.

Preparatory School in Economics, Business and Management Sciences, Department of Mathematics, Tlemcen, Algeria,[email protected]


33 Bilinear Multipliers of Weighted Wiener Amalgam Spacesand Variable Exponent Wiener Amalgam SpacesOznur Kulak and A.Turan Gurkanlı

Let ω1, ω2 be slowly increasing weight function and let ω3 be any weight function on Rn. Assume thatm (ξ, η) is a bounded function on Rn× Rn. We define

Bm (f, g) (x) =

∫Rn

∫Rn

∧f (ξ)

∧g (η)m (ξ, η) e2πi〈ξ+η,x〉dξdη

for all f, g εC∞c (Rn), where C∞c (Rn) denotes the space of infinitely differentiable complex-valued func-tions with compact support on differentiable Rn. Also let W

(Lp1 , Lq1ω1

), W

(Lp2 , Lq2ω2

)and W

(Lp3 , Lq3ω3

)be Wiener amalgam spaces. We say that m (ξ, η) is a bilinear multiplier on Rn of type (W (p1, q1, ω1; p2, q2,ω2; p3, q3, ω3)) if Bm is bounded operator from W

(Lp1 , Lq1ω1

)× W

(Lp2 , Lq2ω2

)to W

(Lp3 , Lq3ω3

)where 1 ≤

p1 ≤ q1 <∞, 1 ≤ p2 ≤ q2 <∞ , 0 < p3, q3 ≤ ∞ . We denote by BM (W (p1, q1, ω1; p2, q2, ω2; p3, q3, ω3))the vector space of bilinear multipliers of type (W (p1, q1, ω1; p2, q2, ω2; p3, q3, ω3)). In the First Section ofthis work, we investigate some properties of this space and we give some examples of these bilinear multi-pliers. In the Second Section , by using variable exponent Wiener amalgam spaces we define the bilinearmultipliers of type (W (p1 (x) , q1, ω1; p2 (x) , q2, ω2; p3 (x) , q3, ω3)) from W

(Lp1(x), Lq1ω1

)×W

(Lp2(x), Lq2ω2

)to W

(Lp3(x), Lq3ω3

)where p1 (x) ≤ q1, p2 (x) ≤ q2, p∗1, p∗2, p∗3 <∞ for all p1 (x) , p2 (x) , p3 (x) εP (Rn). We

denote by BM (W (p1 (x) , q1, ω1; p2 (x) , q2, ω2; p3 (x) , q3, ω3)) the vector space of bilinear multipliers oftype (W (p1 (x) , q1, ω1; p2 (x) , q2, ω2; p3 (x) , q3, ω3)). Similarly, we discuss some properties of this space.

Some key references are given below.

References

[1] Aydın, I, Gurkanlı, A. T: Weighted variable exponent amalgam spaces. Glasnik Mathematicki.47(67), 165-174 (2012)

[2] Bennett, C, Sharpley, R: Interpolation of Operators. Academic Press (1988)

[3] Blasco, O: Notes on the spaces of bilinear multipliers. Rev. Un. Mat. Argentina. 50(2), 23-37 (2009)

[4] Dobler, T: Wiener Amalgam Spaces on Locally Compact Groups, Master’s Thesis, University ofViena (1989).

[5] Feichtinger, H. G: A characterization of Wiener’s algebra on locally compact groups, Arch. Math.(Basel), 29, 136-140 (1977)

[6] Feichtinger, H. G: Banach convolution algebras of Wiener type functions, series, operators, Proc.Conf. Budapest 38, Colloq. Math. Soc. Janos. Boyai., 509-524 (1980)

[7] Feichtinger, H. G: Banach spaces of distribution of Wiener’s type interpolation, Proc. Conf. Funct.Anal. Approx., Oberwolfach, 60, Birkhauser, Basel, 153-165 (1981)

[8] Kulak, Oznur, Gurkanlı A.Turan: Bilinear multipliers of weighted Lebesgue spaces and variableexponent Lebesgue spaces, Journal of Inequalities and Applications 2013, 2013:259, 1-21 (2013).

Oznur Kulak: Ondokuz Mayıs University, Faculty of Arts and Science, Department of Mathematics, Kurupelit, Atakum,Samsun-Turkey, [email protected]

A.Turan Gurkanlı: Istanbul Arel University, Faculty of Science and Letters , Department of Mathematics and computerSciences, Tepekent, Buyukcekmece-Istanbul, [email protected]

This work was supported by the Ondokuz Mayıs University, Project number PYO.FEN.1904.13.002


34 Global Optimization Problem of Lipschitz Functions Usingα-Dense CurvesDjaouida Guettal and Mohamed Rahal

In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. Theclassical multidimensional global optimization methods involves great difficulties for their implementationto high dimensions. The Alienor method allows to transform a multivariable function into a function ofa single variable for which it is possible to use efficient and rapid method for calculating the the globaloptimum. This simplification is based on the using of a reducing transformation called Alienor.

References

[1] Y. Cherruault, Optimisation: Methodes locales et globales, Presses Universitaire de France, 1999.

[2] R. Horst and H. Tuy, Global Optimization, Deterministic Approach, Springer-Verlag, Berlin, 1993.

[3] G. Mora and Y. Cherrualult, Characterization and Generation of α-dense Curves, Comp. and Math.with Applic. Vol. 33, No.9, p.p. 83-91, 1997.

[4] G. Mora, Y. Cherrualult and A. Ziadai, Functional Equations Generating Space-Densifing Curves,Comp. and Math. with Applic. 39, p.p. 45-55, 2000.

[5] A. Torn and A. Silinkas, Global Optimization, Springer-Verlag, New york, 1988.

[6] A. Ziadi and Y. Cherruault, Generation of α-dense curves and application to global optimization,Kybernetes, Vol. 29 No.1, pp.71-82,2000.

[7] A. Ziadi, Y. Cherruault and G. Mora, Global Optimization, a New Variant of the Alienor Method,Comp. and math. with Applic. 41, p.p. 63-71, 2001.

[8] S. A. Piyavsky, An algorithm for finding the absolute extremum for a function. USSR Comput.Mathem. and Mathem. Phys., 12, No.4, 888-896. 1972.

[9] A. Ziadi and Y. Cherruault, Generation of α-dense Curves in a cube of Rn, Kybernetes Vol. 27 No.4,pp. 416-425, 1998.

Guettal Djaouida and Rahal Mohamed: Laboratory of Fundamental and Numerical Mathematics Department of Math-ematics, University Ferhat Abbas of Setif 1, Algeria , [email protected], mrahal [email protected]


35 Estimating 2-D GARCH Models by Quasi-Maximum Likeli-hoodSoumia Kharfouchi

The introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model in the famous paper of Engel (1982)was a natural starting point in modeling the temporal dependencies in the conditional variance of financial time series. Thismodel allow the variance to depend on the past of the random process. Since, numerous variants and extensions of thismodel have been proposed. Generalized ARCH (GARCH) model is the main natural extension of this model, the passagehas been done in a way that is similar to the passage from the AR model to the ARMA one. A large strand of the financialliterature is devoted to one-dimensional GARCH model; see for example Bellerslev (1986), Bellerslev , Engle and Nelson(1994), Palm (1996), Shephard (1996). Next, this GARCH model has seen many extensions with the introduction of laggedvalues of the variance or models allowing to take into account the phenomena of asymmetry such as EGARCH models(Exponential GARCH) proposed by Nelson (1991), TGARCH models (Threshold GARCH) proposed by Zakoian (1991),or again DCC-MVGARCH models (Multivariate GARCH with Dynamical Conditional Correlation) proposed by Engle andSheppard (2001). The treatment of spatial interaction (dependence) and spatial structure (heterogeneity) in practice maybe modeled by some random fields (Xt)t∈Zd . Noiboar and Cohen (2005) had the idea of extending the one-dimensionalGARCH model into two-dimensions in order to take into account the variability of the variance trough the space. Theycould also show that the two-dimensional GARCH model generalizes the causal Gauss Markov Random Field (GMRF),largely used in clutter modeling with the disadvantage of having a constant conditional variance trough the space whichmakes the use of a GARCH clutter modeling better than the use of a GMRF one. This phenomena is often found onnatural images because they are corrupted due to several factors, such as performance of imaging sensors and characteristicsof the transmission channel (Amirmazlaghani and Amindavar (2010)). Furthermore, data of textural information such asimages of geographical regions that allow the production of some maps, and in general, a lot of images of the earth arecharacterized by a behavior in cluster of the space variability (clustering of innovations) i.e. significant changes tend tofollow big changes small changes tend to follow small changes; it is clearly seen in the image it self where the decreaseof the level of gray calls a decrease. On the other hand, research on statistical properties of images wavelet coefficientshave shown that the marginal distribution of wavelet coefficients are highly kurtotic, and can be described using suitableheavy-tailed distribution (cf. Achim et al 2003). Indeed, Amirmazlaghani and Amindavar (2009) shown that the subbanddecomposition of SAR images has significantly non-gaussian statistics that are best described by the 2-D GARCH model.It should be noted that statistical and probabilistic properties as well as building the parameter estimates have been gainedmore attention for the spatial linear models than the nonlinear one, despite of the well known nonlinearity structure ofmany spatial series, this is partly due to the fact that the existence of spatial dependence creates difficulties for buildingsuch estimates. So, the purpose of this paper is to present the quasi-maximum likelihood (QML) method which provides,for GARCH models, theoretical framework for proving efficiency of estimators under mild regularity conditions, but withno moment assumptions on the observed process. Consistency and the asymptotic normality of the QML estimators ofcoeffients of 2-D GARCH are derived under optimal conditions.

References[1] Achim, A., Bezerianos, A., and Tsakalides, P. (2003). “SAR image denoising via Bayesian wavelet shrinkage based on

heavy tailed modeling”. IEEE Transaction on Geoscience and Remote Sensing, 41 (8), 1773-1784.

[2] Amirmazlaghani, M., Amindavar, H. (2010). Image denoising using two-dimensional GARCH model. Systems, Signalsand image processing, 397-400.

[3] Amirmazlaghani, M., Amindavar, H., and Moghaddamjoo A. (2009). “Speckle Suppression in SAR Images Using 2-DGARCH Model”. IEEE Trans. Image Processing, 18 (2), 250-259.

[4] Shephard, N. (1996). Statistical aspects of ARCH and stochastic volatility. in: Cox, D. R., O. E. Barndor -Nielsen & D.V. Hinkley, eds., Statistical Models in Econometrics, Finance and other fields, 1-67.

[5] Tjostheim, D. (1978). Statistical spatial series modelling I. Adv. App. Prob. 10, 130-154.

[6] Tjostheim, D. (1983). Statistical spatial series modelling II. Adv. App. Prob. 15, 562-584.

[7] Whittle, P. (1954) On stationary process in the plane. Biometrika 41, 434 - 449.

Departement de Medecine, Universite 3 Constantine, Algeria, s [email protected]


36 An Approach Using Stream Ciphers Algorithm for SpeechEncryption and DecryptionBelmeguenai Aissa, Mansouri Khaled and Lashab Mohamed

In this work, we have done an e cient implementation of stream ciphers algorithm for speech data encryption and decryption.The stream cipher algorithm is proposed. The design based on linear feedback shift register (LFSR) whose polynomial isprimitive and nonlinear Boolean function. At first three speech signal were recorded from different speakers and were savedas wav file format. Then our developed program was used to transform the original speech signal wav file into positive signaldata, and transform the positive data signal into positive digital signal file. Finally, we used our implemented program toencrypt and decrypt speech data. We conclude the paper by showing that The design can resist to certain known attacks.

References[1] Md. M. Rahman, T. K. Saha and Md.A. Bhuiyan, Implementation of RSA Algorithm for Speech Data Encryption and

Decryption, International Journal of Computer Science and Network Security IJCSNS, vol. 12, no. 3, 2012, pp. 74-82.

[2] K. Merit1 and A. Ouamri, Securing Speech in GSM Networks using DES with Random Permutation and InversionAlgorithm, International Journal of Distributed and Parallel Systems (IJDPS) Vol.3, No.4, 2012.

[3] A. Musheer, A. Bashir and F. Omar, Chaos Based Mixed Key Stream Genrator for Voice Data Encryption, InternationalJournal on Cryptography and Information Security (IJCIS),Vol.2, No.1,March 2012.

[4] H. Kohad , V.R.Ingle and M.A.Gaikwad, Security Level Enhancement In Speech Encryption Using Kasami Sequence,International Journal of Engineering Research and Applications (IJERA) , V 2, 2012, pp.1518-1523.

[5] M. Ashtiyani , P. Moradi Birgani , S. S. Karimi Madahi, Speech Signal Encryption Using Chaotic Symmetric Cryp-tography, Journal of Basic and Applied Scienti c Research, pp. 1668- 1674, 2012.

[6] C. Carlet, On the cost weight divisibility and non linearity of resilient and correlation immune functions, Proceedingof SETA01 (Sequences and their applications 2001), Discrete Mathematics, Theoretical Computer Science, Springer p131-144, 2001.

[7] P.Van Oorschot A. Menezes and S. Vantome, Handbook of Applied Cryptography, http://www.cacr.math.uwterloo/hac /,1996.

[8] G.Ars, Une application des bases de Grobner en Cryptographie, DEA de Rennes I, 2001.

[9] Y. V. Tarannikov, On resilient Boolean functions with maximum possible nonlinearity, Proceedings of INDOCRYPT2000, lecture Notes in Computer Science 1977, pp19-30, 2000.

[10] E. Filiol and C. Fontaine, Highly nonlinear balanced Boolean function with a good correlation-immunity, In: Advancesin cryptology- EUROCRYPT98, lecture Notes in Computer Science, N 1403. Pp475-488, Springer-Verlag, 1988.

[11] D. K. Dalai, On Some Necessary Conditions of Boolean Functions to Resist Algebraic Attacks, thesis, 2005.

[12] E.R Berlekamp, Algebraic Coding Theory, Mc Grow- Hill, New- York, 1968.

Laboratoire de Recherche en Electronique de Skikda, Universite 20 Aout 1955-Skikda, BP 26 Route d El-hadaeik Skikda,Algeria


37 A Generalized Statistical Convergence for Sequences of Setsvia IdealsOmer Kisi and Ekrem Savas

The notion of statistical convergence of sequences of numbers was introduced by Fast [1] and Schoenberg [5] independently.Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis,Number Theory. Later on, statistical convergence turned out to be one of the most active ares of research in summabilitytheory after the works of Fridy [2] and Salat [4] . In last few years, many generalization of statistical convergence haveappeared.

The concept of I−convergence of real sequences is a generalization of statistical convergence which is based on the struc-ture of the ideal I of subsets of the set of natural numbers. P. Kostyrko et al. [3] introduced the concept of I−convergenceof sequences in a metric space and studied some properties of this convergence.

In this study, we make a new approach to the notions of [V, λ]−summability and λ−statistical convergence of sequenceof sets by using ideals and introduce new notions, namely, I − [V, λ]−summability, Iλ−statistical convergence of sequenceof sets. We mainly examine the relation between these two methods and also the relation between I − [V, λ]−summability,Iλ−statistical convergence of sequence of sets are introduced by the authors recently.

References[1] H. Fast, Sur la convergence statistique, Collog. Math. 2 (1951) 241-244.

[2] J. A. Fridy, On statistical convergence, Analysis, 5 (1985)301-313.

[3] P. Kostyrko, T. Salat, W.Wilczynski, I−convergence, Real Anal. Exchange, 26(2) (2000/2001), 669-686.

[4] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.

[5] Schoenberg, I.J. (1959). The integrability of certain functions and related summability methods. Amer. Math. Monthly,66: 361-375.

Omer Kisi: Faculty Of Education, Mathematics Education Depertmant, Cumhuriyet University, Sivas, Turkey, [email protected], [email protected]

Ekrem Savas: Istanbul Ticaret University, Deparment of Mathematics, Uskudar, Istanbul, Turkey, ekremsavas@yahoo


38 Some Embedding Questions for Weighted Difference SpacesLeili Kussainova and Ademi Ospanova

We introduce weighted space w2p (υ) which is a difference analogue of weighted Sobolev space W 2

p (υ) (1 ≤ p < ∞). A

compactness question for operator A : w2p (υ)→ lq (u) acting from w2

p (υ) into the space of sequences lq (u) (1 < p ≤ q <∞)is investigated. Also estimates of approximation numbers for the embedding operator A are considered. Besides, it ispossible to apply these research methods to the spectral theory of difference analogues of differential operators.

References[1] B. Musilimov, M. Otelbaev, Estimate of the least eigenvalue of a class of matrices that corresponds to the Sturm-

Liouville difference equation, Zh. Vychisl. Mat. i Mat. Fiz., 21 (1981), no. 6, 1430-1434 (Russian),

[2] E. Z. Grinshpun, M. Otelbaev, Smoothness of the solution to the Sturm-Liouville equation in L1 (−∞,∞), Izv. ANKazSSR, Ser. phys.-mat, no 5 (1984), 26-29 (Russian),

[3] K. T. Mynbayev, M. O. Otelbayev, Weighted functional spaces and differential operators spectrum, Moscow, Nauka,1988 (Russian),

[4] E. S. Smailov, Difference embedding theorems for weighted Sobolev spaces and their applications, Soviet Math. Dokl.,vol. 270, no 1 (1983), 52-55 (Russian, English),

[5] G. Muchamediev, Spectrum of a difference operator and some embedding theorems, Kraevye zadachi dlya dif. ur. i ichprilozh. v mechanike i technike, Alma-Ata, Nauka (1983), 104-105 (Russian),

[6] R. Oinarov, A. P. Stikharnyi, Criteria for the boundedness and compactness of a difference inclusion, Mat. Zametki,50 (1991), no. 5, 54-60; translation in Math. Notes 50 (1991), no. 5-6, 1130-1135 (Russian, English),

[7] A. T. Bulabaev, A. T. Muchambetzhanov, Embedding theorems for some multi-dimensional spaces, Izv. AN RK, ser.phys.-mat., no 3 (1992) (Russian),

[8] A. T. Bulabaev, A. T. Muchambetzhanov, On some difference embedding theorems, Sbornik KazGNU (1993) (Russian),

[9] M. S. Bichegkuev, On the spectrum of difference and differential operators in weighted spaces, Funktsional. Anal. iPrilozhen., 44 (2010), no. 1, 80-83; translation in Funct. Anal. Appl. 44 (2010), no. 1, 65-68 (Russian, English),

[10] A. G. Baskakov, Spectral analysis of differential operators with unbounded operator-valued coefficients, differencerelations, and semigroups of difference relations, Izv. Ross. Akad. Nauk Ser. Mat. 73 (2009), no. 2, 3-68; translationin Izv. Math. 73 (2009), no. 2, 215-278 (Russian, English),

[11] M. Otelbaev, L. K. Kussainova, Spectrum estimates for one class of differential operators, Sbornik trudov Ins-ta matem.NAN Ukraine Operators theory, differential equation and function theory, vol. 6, no. 1 (2009), 165-190 (Russian),

[12] L. Kussainova, A. Ospanova, An Embedding Theorem for Difference Weighted Spaces, to appear in Proceedings of TheWorld Congress on Engineering, 2014 .

Leili Kussainova: L. N. Gumilyov Eurasian National University, Department of Mechanics and Mathematics, Astana,010008 Kazakhstan, [email protected]

Ademi Ospanova: L. N. Gumilyov Eurasian National University, Department of Theoretical Informatics, Astana, 010008Kazakhstan, [email protected]


39 On (λ, I)−Statistical Convergence of Order α of Sequencesof FunctionHacer Sengul and Mikail Et

In this talk, we introduce and examine the concepts of pointwise (λ, I)−statistical convergence of order α and pointwisewp (f, λ, I)−summability of order α of sequences of real valued functions and we investigated between their relationship.We aim some notions and results from the statistical convergence of order α of sequences of function are extended to theI−convergence of order α of sequences of function.

References[1] Connor, J. S. The Statistical and strong p−Cesaro convergence of sequences, Analysis 8 (1988), 47-63,

[2] Colak, R. Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India:Anamaya Pub, 2010: 121–129,

[3] Savas, Ekrem; Das, Pratulananda. A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), no. 6,826–830,

[4] Salat, T. ; Tripathy, B. C. and Ziman M. On I−convergence field, Ital. J. Pure Appl. Math. No. 17 (2005), 45–54,

[5] Kostyrko, P. ; Salat, T. and Wilczynski, W. I−convergence, Real Anal. Exchange 26 (2000/2001), 669-686,

[6] Et, M. ; Altınok, H. and Altın, Y. On generalized statistical convergence of order α of difference sequences, J. Funct.Spaces Appl. 2013, Art. ID 370271, 7 pp,

[7] Et, M. ; Cınar, M. and Karakas, M. On λ−statistical convergence of order α of sequences of function, J. Inequal. Appl.2013, 2013:204, 8 pp,

[8] Mursaleen, M. λ−statistical convergence, Math. Slovaca, 50(1) (2000), 111-115,

[9] Colak, R. and Bektas C. A. λ −statistical convergence of order α, Acta Mathematica Scientia 31(3) (2011) , 953-959.

Hacer Sengul: Siirt University, Faculty of Science, Department of Mathematics, Siirt-Turkiye, [email protected] Et: Firat University, Faculty of Science, Department of Mathematics, Elazig-Turkiye, [email protected]


40 Range Kernel Orthogonality of Generalized DerivationsMessaoudene Hadia

Let L (H) be the algebra of all bounded linear operators acting on a complex separable and infinite dimensional Hilbert spaceH. For operators A,B,X ∈ L(H), we define the generalized derivation δA,B associated with (A,B) by δA,B(X) = AX−XBfor X ∈ L(H).

The purpose of this work is to find for wich operators A,B ∈ L(H) we have:

||T − (AX −XB)|| ≥ ||T ||for all X ∈ L(H) and for all T ∈ kerδA,B .

Faculty of Economics sciences and Management, University of Tebessa-Algeria, [email protected]


41 On Stancu Variant of q-Baskakov-Durrmeyer Type Opera-torsP.N.Agrawal and A.Sathish Kumar

In recent years, one of the most interesting areas of research in approximation theory is the application of q- calculus. Phillips[8], first introduced the q-analogue of well known Bernstein polynomials. Subsequently, several researchers proposed the q-analogues of exponential, Kantorovich and Durrmeyer type operators. Recently q-Baskakov operators and their Kantorovichand Durrmeyer variants have been studied in [3, 1] and [2] respectively. Stancu [?] introduced a generalization of Bernstein

polynomials by defining the positive linear operators P(α,β)n : C[0, 1] → C[0, 1] by P

(α,β)n (f, x) =

∑nk=0 bn,k(x)f

(k+αn+β

),

where bn,k(x) =(nk

)xk(1− x)n−k and α, β are any two real numbers which satisfy the condition 0 ≤ α ≤ β. If α = β = 0,

the above sequence of operators reduces to Bernstein polynomials. His work led many researchers to consider similar typeof modification of various sequences of operators. In 2012, the authors [?] studied some approximation properties of theBaskakov-Durrmeyer-Stancu operators. Recently, we [1] introduced the q-analogue of Bernstein-Schurer-Stancu operatorsand discussed the local and global approximation results for these operators. To approximate Lebesgue integrable functionson the interval [0,∞), Agrawal and Thamer [2] introduced the following operators:

Mn(f(t);x) = (n− 1)

∞∑k=1

pn,k(x)

∫ ∞0

pn,k−1(t)f(t)dt+ (1 + x)−nf(0), (41.1)

where pn,k(x) =(n+ k − 1

k

)xk(1 + x)−(n+k), x ∈ [0,∞). The rate of pointwise approximation by the operators (41.1)

for functions of bounded variations was considered by Gupta in [5]. Later on, Gupta and Abel [6] proposed the Bezier-Durrmeyer integral variant of the operators (41.1) and studied the rate of convergence for functions of bounded variation.In the present paper, we propose to study the approximation properties for the Stancu type modification of Baskakov-Durrmeyer operators given by (41.1) based on q-integers. Let α, β be any two real numbers such that 0 ≤ α ≤ β, q ∈ (0, 1),n ∈ N and f ∈ Cγ [0,∞) = f ∈ C[0,∞) : f(t) = O(tγ)as t→∞, for some γ > 0, the q-analogue of the Stancu variant ofthe operators (41.1) is defined as follows:

Mα,βn,q (f, x) = [n− 1]q

∞∑k=1

pqn,k(x)

∫ ∞/A0

qk−1pqn,k−1(t)f

([n]qt+ α

[n]q + β

)dqt+ pqn,0(x)f

(α

[n]q + β

), (41.2)

where pqn,k(x) =(n+ k − 1

k

)qqk(k−1)

2xk

(1 + x)(n+k)q

, x ∈ [0,∞). In the case, α = β = 0 and q → 1−, the above operators

(41.2) reduce to (41.1). The purpose of this paper is to study some approximation properties of the operators defined in(41.2). First, we give the basic convergence theorem and then obtain Voronovskaja type theorem. Subsequently, we studythe local approximation results and then obtain the rate of convergence in terms of the weighted modulus of continuity.Also, we study the A-statistical convergence of these operators. Finally, we consider a modification of the operators (41.2),following King’s approach to get a better approximation.

References[1] P. N. Agrawal, V. Gupta and A. Sathish Kumar, On q-analogue of Bernstein-Schurer-Stancu operators, Appl. Math.

Comput. 219 (2013) 7754-7764.

[2] P. N. Agrawal and K. Thamer, Approximation of unbounded functions by a new sequence of linear positive operators,J. Math. Anal. Appl. 225 (1998) 660-672.

[3] A. Aral and V. Gupta, Generalized q-Baskakov operators, Math. Slovaca. 61 (4) (2011) 619-634.

[4] A. Aral and V. Gupta, On the Durrmeyer type modification of the q Baskakov type operators, Nonlinear Anal.: TheoryMethods Appl. 72 (2010) 1171-1180.

[5] V. Gupta, Rate of approximation by a new sequence of linear positive operators, Comput. Math. Appl. 45 (12) (2003)1895-1904.

[6] V. Gupta and U. Abel, Rate of convergence of bounded variation functions by a Bezier-Durrmeyer variant of theBaskakov operators, IJMMS. 9 (2004) 459-469.

[7] V. Gupta and C. Radu, Statistical approximation properties of q-Baskakov-Kantorovich operators. Cent. Eur. J. Math.8 (1) (2009) 809-818.

[8] G. M. Phillips, Bernstein polynomials based on the q−integers, The heritage of P.L. Chebyshev: A Festschrift in honorof the 70th-birthday of Professor T.J. Rivlin., Ann. Numer. Math. 4 (1997) 511-518.

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India, pna [email protected],[email protected]

Dedicated to Prof. R. P. Agarwal on his 67th birthday.


42 Generalised Baskakov Kantorovich OperatorsP.N.Agrawal and Meenu Goyal

For f ∈ L1[0, 1] (class of Lebesgue integrable functions on [0, 1]), Kantorovich introduced the operators

Kn(f ;x) = (n+ 1)

n∑ν=0

pn,ν(x)

∫ 1

0χ(t)f(t)dt,

where pn,ν(x) =(nν

)xν(1 − x)n−ν , x ∈ [0, 1] is the Bernstein basis function and χ(t) is the characteristic function of the

interval

[νn+1

, ν+1n+1

].

Many authors have studied the approximation properties of these operators. subsequently, several authors have proposedthe Kantorovich-type modification of different linear positive operators and studied their approximation properties.Recently in [1], Erencin defined the Durrmeyer type modification of generalised Baskakov operators introduced by Mihesan[2], as

Ln(f ;x) =

∞∑k=0

Wan,k(x)

1

B(k + 1, n)

∫ ∞0

tk

(1 + t)n+k+1f(t)dt, x ≥ 0,

where Wan,k(x) = e

−ax1+x Pk(n,a)

k!xk

(1+x)n+k , pk(n, a) =

k∑i=0

(nk

)(x)ia

k−i, and (x)0 = 1, (x)i = x(x + 1)...(x + i − 1) for i ≥ 1.

Inspired by the above work, we consider the Kantorovich type modification of generalised Baskakov operators for the functionf defined on Cγ [0,∞) := f ∈ C[0,∞) : |f(t)| ≤M(1 + t)γ for some M > 0, γ > 0 as follows :

Kan(f ;x) = (n+ 1)

∞∑k=0

Wan,k(x)

∫ k+1n+1

kn+1

f(t)dt, a ≥ 0. (42.1)

The purpose of this paper is to study some local direct results, degree of approximation for a Lipschitz type space, approx-imation of continuous functions with polynomial growth, simultaneous approximation properties for the operators definedin (42.1). In the last section, we construct the bivariate case for these operators and then discuss the rate of convergence interms of the modulus of continuity.

References[1] A. Erencin, Durrmeyer type modification of generalized operators, Appl. math. comput. (218) (2011) 4384-4390.

[2] V. Mihesan, Uniform approximation with positive linear operators generated by generalised Baskakov method, Automat.Comput. Appl. Math. (1) (1998) 34-37.

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India, pna [email protected],[email protected]


43 Approximate Solutions of Fractional Order Boundary ValueProblems by a Novel MethodAli Akgul

An approximate solution of a fractional order two-point boundary value problem (FBVP) is given in this work. We usethe reproducing kernel Hilbert space method. In order to illustrate the applicability and accuracy of the present method,the method is applied to some examples. The results are compared with the ones obtained by the Cubic splines andsinc-Galerkin methods. There are only a few studies regarding the application of reproducing kernel method to fractionalorder differential equations. Therefore, this study is going to be a new contribution and highly useful for the researchersin fractional calculus area of scientific research. Results of numerical examples show that the presented method is veryeffective.

References[1] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68:337 404, 1950,

[2] M. Cui, Y. Lin, Nonlinear numerical analysis in the reproducing kernel space. Nova Science Publishers Inc.,New York,2009,

[3] M. Inc, A. Akgul, The reproducing kernel Hilbert space method for solving Troeschs problem, Journal of the Associationof Arab Universities for Basic and Applied Sciences, (2013) 14, 19-27,

[4] I. Podlubny, Fractional di erential equations, volume 198 of Mathematics in Science and Engineering, Academic Press,Inc., San Diego, CA, 1999,

[5] A. Secer, S. Alkan, M. A. Akinlar, and M. Bayram, Sinc- Galerkin method for approximate solutions of fractional orderboundary value problems., Boundary Value Problems, 2013: 1–14.

Dicle University, Faculty of Education, Department of Mathematics, Diyarbakir-Turkiye, [email protected] work was supported by Dicle University


44 Some Power Series on Archimedean and Non-ArchimedeanFieldsFatma Calıskan

In the present study, we proved that the theorem which was established in complex (Archimedean) field and p-adic (non-Archimedean) field has an analogue in the formal Laurent series (non-Archimedean) field over a finite field. Hence we showthat some power series in the formal Laurent series field on the finite field F take values either Liouville or from F(x) forLiouville arguments under certain conditions, where F(x) is the quotient field of the polynomial ring F[x] on the finite fieldF.

References[1] P. Bundschuh,Transzendenzmasse in Korpern formaler Laurenteihen, J. Reine Angew Math. 299/300 (1978), 411-432,

[2] E. Dubois,On Mahler’s Classification in Laurent Series Fields, Rocky Mt. J. of Math. 26 (1996), 1003-1016,

[3] K. Mahler,Zur Approximation der Exponantialfunktion und des Logarithmus I, J. Reine Angew Math. 166 (1932),137-150,

[4] K. Mahler,Uber eine Klassen-Einteilung der p-Adischen Zahlen,Mathematica Leiden 3 (1961), 177-185,

[5] M. H. Oryan, Uber gewisse Potenzreihen deren Funktionswerte fur Argumente aus der Menge der Liouvilleschen zahlenU-zahlen vom Grad ≤ m sind, Istanbul Univ. Fen Fak. Mec. Seri A 47 (1983-86), 15-34,

[6] M. H. Oryan, Uber gewisse Potenzreihen deren Funktionswerte fur Argumente aus der Menge der p-adischen Liou-villeschen zahlen p-adische U-zahlen vom Grad ≤ m sind, Istanbul Univ Fen Fak. Mecm. Seri A, 47 (1983-86), 53-67.

Istanbul University, Faculty of Science, Department of Mathematics, 34134 Vezneciler/Istanbul, Turkey, fatmac@ istan-bul.edu.tr


45 Existence and Monotone Iteration of Symmetric Positive So-lutions for Integral Boundary-Value Problems with φ-Lapla-cian OperatorTugba Senlik and Nuket Aykut Hamal

The purpose of this talk is to investigate the existence and iteration of symmetric positive solutions for integral boundary-value problem. An existence result of positive, concave and symmetric solutions and its monotone iterative scheme areestablished by using the monotone iterative technique. An example is worked out to demonstrate the main result.

References[1] H. Feng, Triple symmetric positive solutions for multipoint boundary-value problem with one-dimensional p-Laplacian,

Math. Comput. Model. 47 (2008), 186-195,

[2] Y. Ding, Monote Iterative Method for Obtaining Positive Ssolutions of Integral Boundary-Value Problems with φ-Laplacian Operator, Electron. J. Dif. Equ., 219 (2012), 1-9,

[3] M. Pei, S.K. Chang, Monotone iterative technique and symmetric positive solutions for a fourth-order boundary valueproblem, Math. Comput. Model. 51 (2010), 1260-1267,

[4] H. Pang, Y. Tong, Symmetric positive solutions to a second-order boundary value problem with integral boundaryconditions, Bound. Value Probl., 2013:150,

[5] Y. Cui, Y. Zou, Monotone iterative method for differential systems with coupled integral boundary value problems,Bound. Value Probl., 2013:245,

Tugba Senlik: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir- Turkey, [email protected]

Nuket Aykut Hamal: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir-Turkey, [email protected]


46 Analytical Calculation of Partial Differential Equations Ap-plied to Electrical Machines With Ideal Halbach PermanentMagnetsMourad Mordjaoui, Ibtissam Bouloukza and Dib Djalel

Recently several electrical machines and devices use high energy permanent magnets with different direction of flux penetra-tion. For the design and dimensioning of these electromechanical systems, we must know the distribution of the magneticfield in each part of the magnetic system and in particular at the air gap in which the energy conversion takes place.Generally, Maxwell’s partial differential equations supplemented by material’s law are used to describe the magnetic fieldproblems. However, a numerical calculation is necessary, especially with the complex geometry of these devices. This paperdeals with an analytical calculation of magnetic field distribution of iron-cored internal rotor of surface mounted permanentmagnetic synchronous motor with ideal Halbach magnetization. A Halbach array is a special arrangement of permanentmagnets that concentrates the magnetic flux lines on one side while reducing the flux lines on the other side to nearly zero.The model is based on evaluation and calculation of governing partial differential equations at no load conditions. Bothfield and magnetic induction in airgap and magnet are presented. Results obtained are compared with those obtained byfinite-element analysis.

References[1] K. Halbach, “Design of permanent multipole magnets with oriented rare earth cobalt material,” Nucl. Instrum. Methods,

vol. 169, pp. 1–10, 1980.

[2] Y. N. Zhilichev, “Analytic solutions of magnetic field problems in slotless permanent magnet machines,” Int. J. Comput.Math. Elect. Electron. Eng., vol. 19, no. 4, pp. 940–955, 2000.

[3] A. Rahideh, and T. Korakianitis, “Analytical Magnetic Field Distribution of Slotless Brushless Machines with InsetPermanent Magnets”, IEEE Trans. Magn., vol. 47, no. 06, pp. 1763–1774, Jun. 2011.

[4] P-D. Pfister, .and Y. Perriard “Slotless Permanent-Magnet Machines: General Analytical Magnetic Field Calculation”,IEEE Trans. Magn., vol. 47, no. 06, pp. 1739–1752, Jun. 2011.

[5] A. Rahideh, and T. Korakianitis, “Analytical calculation of open-circuit magnetic field distribution of slotless brushlessPM machines”, Electrical Power and Energy Systems 44 (2013) 99–114

[6] M. Marinescu and N. Marinescu, “New concept of permanent magnet excitation for electrical machines—Analytical andnumerical computation,” IEEE Trans. Magn., vol. 28, pp. 1390–1393,

[7] Z. P. Xia, Z. Q. Zhu, and D. Howe, “Analytical Magnetic Field Analysis of Halbach Magnetized Permanent-MagnetMachines”, IEEE Trans. Magn., vol. 44, no. 04, pp. 1864–1872, Jul. 2004.

Mourad Mordjaoui: Electrical Engineering Department, University of 20 August 1955. Skikda. 21000. Algeria, mord-jaoui mourad @yahoo.fr

Ibtissam Bouloukza: Electrical Engineering Department, University of 20 August 1955. Skikda. 21000. Algeria,Boulekza [email protected]

Dib Djalel: Electrical Engineering Department, University of Tebessa. Tebessa, Algeria, [email protected]


47 Principal Functions of Differential Operators with SpectralParameter in Boundary ConditionsNihal Yokus

In this talk, we investigate the principal functions corresponding to the eigenvalues and the spectral singularities of theboundary value problem

−y′′

+ q(x)y = λ2y, x ∈ R+ = [0,∞) ,

and (α0 + α1λ+ α2λ

2)y′(0)−

(β0 + β1λ+ β2λ

2)y (0) = 0,

where q is a complex valued function and αi, βi ∈ C, i = 0, 1, 2 with α2, β2 6= 0.

References[1] M. A. Naimark, Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operator of second

order on a semi-axis, Amer. Math. Soc. Trans. Ser.2. Vol.16 (1960), 103-193.

[2] E.P.Dolzhenko, Boundary value uniqueness theorems for analytic functions, Math. Notes 26 (1979), 437-442.

[3] V. A. Marchenko, Expansion in eigenfunctions of non-selfsdjoint singular second order differential operators, Amer.Math. Soc. Transl. Ser. 2 25(1963) 77-130.

[4] V. E. Lyance, A differential operator with spectral singularities I,II, Amer. Math. Soc. Trans., Ser.2, Vol.60 (1967),185-225, 227-283.

Karamanoglu Mehmetbey University, Faculty of Kamil Ozdag Science, Department of Mathematics, Karaman-Turkiye,[email protected]

This is joint work with Turhan Koprubası.


48 Generalized Typically Real FunctionsS.Kanas and A.Tatarczak

Let f(z) = z + a2z2 + · · · be regular in the unit disk and real valued if and only if z is real and |z| < 1. Then f issaid to be typically real function. Rogosinski found the necessary and sufficient condition for a regular function to betypically-real. The main purpose of the presented paper is a consideration of the generalized typically-real functions definedvia the generating function of the generalized Chebyshev polynomials of the second kind

Ψp,q(eiθ; z) =

1

(1− pzeiθ)(1− qze−iθ)=

∞∑n=0

Un(p, q; eiθ)zn,

where −1 ≤ p, q ≤ 1, θ ∈ 〈0, 2π〉, |z| < 1.

References[1] W. Fenchel, Bemerkungen uber die in Einheitskreis meromorphen schlichten Funktionen, Preuss. Akad. Wiss. Phys. -

Math. Kl. 22/23(1931), 431 - 436.

[2] W. Janowski, Extremal problem for a family of functions with positive real part and for some related families, Ann.Polon. Math 23(1970), 159-177.

[3] J. A. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math. J. 9 (1962),25 - 27.

[4] G. Loria,Spezielle Algebraische und Transzendente Ebene Kurven, Tjeorie und Geschichte, Vol. I, transl. F. Schutte,Teubner, Leipzig, 1910.

[5] I. Naraniecka, J. Szynal, A. Tatarczak, The generalized Koebe function, Trudy Petrozawodskogo Universiteta, Matem-atika 17 (2010), 62-66.

[6] I. Naraniecka, J. Szynal, A. Tatarczak An extension of typically-real functions and associated orthogonal polynomials,Ann. UMCS, Mathematica 65(2011), 99-112.

[7] Ch. Pommerenke, Linear-invariant Familien analytischer Funktionen, Mat. Ann. 155 (1964), 108-154.

[8] S. Richardson, Some Hele-Shaw flows with time-dependent free boundaries, J. Fluid Mech. 102 (1981), 263 - 278.

[9] M. S. Robertson, On the coefficients of typically real functions, Bull. Amer. Math. Soc. 41(1935), 565-572.

[10] W. W. Rogosinski, Uber positive harmonische Entwicklungen und typische-reelle Potenzreihen, Math.Z. 35(1932),93-121.

[11] C. Zwikker, The Advanced Geometry of Plane Curves and their Applications, Dover, New York, 1963.

S.Kanas: University of Rzeszow, Faculty of Mathematics and Natural Sciences, ul. S. Pigonia 1, 35-310 Rzeszow,Poland, [email protected]

A.Tatarczak: Maria Curie-Sklodowska University in Lublin, Department of Mathematics, Poland, [email protected]

This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and EngineeringKnowledge, Faculty of Mathematics and Natural Sciences, University of Rzeszow.


49 The Abel-Poisson Summability of Fourier Series in a BanachSpace with Respect to a Continuous Linear RepresentationSeda Ozturk

Let (C,+, .) denote the field of the complex numbers, T be the topological group of the unit circle with respect to theEuclidian topology, H a complex Banach space, α a continuous isometric linear representation of T in H and x an element

of H. In [2,3] a fourier series of x with respect to a continuous isometric linear representation α of the form+∞∑

k=−∞Fk(α, x)

is defined where

Fk(α, x) :=1

2π

+π∫−π

e−iktα(t)(x)dt

for every k ∈ Z, and it is proved that this series converges to x in sense of Cesaro summability method.

In this work, it is directly proved that the series+∞∑

k=−∞Fk(α, x) is Abel-Poisson summable.

References[1] Lybich,Y.I, Introduction to the Theory of Banach Representations of Groups, Birkhauser,Berlin (1988),

[2] Khadjiev.D, Cavus.A, Fourier series in Banach spaces, in: M.M. Lavrentyev (Ed.), Ill-posed and Non-classical Problemsof Mathematical Physics and Analysis, Proc. of the Internat. Conf., Samarkand, Uzbekistan, in: Inverse Ill-posed Probl.Ser., VSP, Utrehct/Boston, 2003, pp. 71–80,

[3] Khadjiev, D., The widest continuous integral. J. Math. Anal. Appl. 326 , 1101-1115 (2007)

[4] Vretblad, A., Fourier Analysis and Its Applications,Springer-Verlag,New York,Inc., 2003.

Karadeniz Technical University, Faculty of Science, Department of Mathematics, Trabzon-Turkey, [email protected]


50 Existence of Solutions for Integral Boundary Value Problemsin Banach SpacesFulya Yoruk Deren and Nuket Aykut Hamal

In this talk, by using the Sadovski fixed point theorem, we establish the existence results of solutions for nonlinear boundaryvalue problems of second order differential equations with integral boundary conditions in Banach spaces.

References[1] R. P. Agarwal, D. O’ Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Acad.,

Dordrecht (2001).

[2] D. Guo, V. Lakshmikantham, X. Liu; Nonlinear Integral Equation in Abstract Spaces, Kluwer Academic publishers,Dordrecht (1996).

[3] Y. Liu, Boundary Value Problems for Second Order Differential Equations on Unbounded Domains in a Banach Space,Appl. Math. Comput. 135, (2003), 569-583.

[4] Y. Liu, Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the WholeLine, Abstract and Applied Analysis, Volume 2012, Article ID 352159.

[5] M. Feng, D. Ji, W. Ge, Positive Solutions for a Class of Boundary Value Problem with Integral Boundary Conditionsin Banach Spaces, Journal of Computational and Applied Mathematics 222, (2008), 351-363.

[6] F. Yoruk Deren, N. Aykut Hamal, Second Order Boundary Value Problems with Integral Boundary Conditions on theReal Line, Electronic Journal of Differential Equations, Vol. 2014 (2014), No. 19, 1-13.

[7] K. Demling; Ordinary Differential Equations in Banach Spaces, Springer-Verlag, Berlin (1977).

Fulya Yoruk Deren: Ege University, Faculty of Science, Department of Mathematics, 35100, Bornova, Izmir-Turkey,[email protected]

Nuket Aykut Hamal: Ege University, Faculty of Science, Department of Mathematics, 35100, Bornova, Izmir-Turkey,[email protected]


51 Existence and Uniqueness Solution of Electro-Elastic An-tiplane Contact Problem with FrictionMohamed Dalah, Khoudir Kibeche, Amar Megrous, Ammar Derbazi

and Soumia Ahmed Chaouache

We study electro-mechanical problem modeling the antiplane shear deformation of a cylinder in frictional contact with a rigidfoundation. The material is assumed to be electro-elastic and the foundation is assumed to be electrically conductive andthe friction is modeled with Tresca’s law. For each problem we present the mathematical model, its variational formulation,and state an existence and uniqueness result.

References[1] Borelli, A., Horgan C.O., Patria, M. C., Saint-Venant’s principal for antiplane shear deformations of linear piezoelectric

materials. SIAMJ. Appl. Math., 62, (2002) 2027–2044.

[2] Chau, O., Dynamic contact problems for viscoelastic materials. Proceedings of Fourteenth International Symposium onMathematical theory of networks and systems., (MTNS 2000), Perpignan (2000).

[3] M. Femond, Adherence des Solides, J. Mecanique Theorique et Appliquee., 6, 383-407 (1987).

[4] Shillor, M., Sofonea, M., Telega, J. J., Models and Analysis of Quasistatic Contact. Lect. Notes Phys., 655, Springer,Berlin Heidelberg, (2004).

[5] Sofonea, M., Essoufi, El H., Quasistatic frictional contact of a viscoelastic piezoelectric body. Adv. Math. Sci. Appl.,14, 613–631 (2004).

[6] Sofonea, M., Dalah, M., Antiplane Frictional Contact of Electro-Viscoelastic Cylinders. Electronic Journal of DifferentialEquations. no. 161, (2007) 1–14.

[7] Sofonea, M., Dalah, M., Ayadi, A., Analysis of an antiplane electro-elastic contact problem. Adv. Math. Sci. Appl., 17,(2007) 385–400.

[8] Dalah, M., Analysis of electro-viscoelastic antiplane contact problem with total slip rate dependent friction. ElectronicJournal of Differential Equations., no. 118, (2009) 1–15 .

Mohamed Dalah: University of Constantine 1, Faculty of Sciences, Department of Mathematics, B.P. 325 Route Ain ElBey, Constantine 25017, Algeria, [email protected]

This work is supported in part by la Direction Generale de la Recherche Scientifique et du Developpement TechnologiqueCNEPRU project & PNR Project, 2011–2013., CODE (valeur) : 8/u250/4506 registered in University Con-stantine 1, Algeria, under grant B00920100136., Title: Modelisation mathematiques pour les problemes Electro-Elastiqueet Visco-Elastique : analyse, optimisation et approche numerique des modA¨es. number UAP(F)-2012/15.


52 Almost Convex Valued Perturbation to Time Optimal Con-trol Sweeping ProcessesDoria Affane and Dalila Azzam-Laouir

We prove existence of solution for first order differential inclusion governed by the sweeping process of the formu(t) ∈ −NK(t)u(t) + F (u(t))u(T ) ∈ K(t)u(0) = u0

(52.1)

where the perturbation F is an upper semicontinuous multifunction with compact almost convex values. Moreover, weprove the existence of solutions to an associate time optimal control problem.

Laboratoire LMPA, Universite de Jijel, [email protected]


53 Evolution Problem Governed by Subdifferential OperatorMustapha Yarou

In the present talk we consider the Cauchy problem for first order differential inclusion of the form

x(t) ∈ F (x(t)) + f(t, x(t)), x(0) = x0 (53.1)

where F is a given set-valued map with nonconvex values and f is a Caratheodory function. The nonconvexity of the valuesof F do not permit the use of classical technique of convex analysis to obtain the existence of solution to this problem(see for instance [2]). One way to overcome this fact is to suppose F upper semicontinuous cyclically monotone, ie. thevalues of F are contained in the subdifferential of a proper convex lower semicontinuous function. The first result is du to[6] when f ≡ 0 and [1] for the problem (53.1) in the finite dimensional setting. An extension of [6] is obtained by [3] and[4] in the finite and infinite dimensional setting, under the assumption that F (x) is contained in the subdifferential of alocally Lipschitz and regular function. A different class of function has been used in [5] to solve the same problem, namelythe authors take F (x) in the proximal subdifferential of a locally Lipschitz uniformly regular function and proved that anyconvex lower semicontinuous function is uniformly regular. We prove that, for locally Lipschitz functions, the class of convexfunctions, the class of lower-C2 functions and the class of uniformly regular functions are strictly contained within the classof regular functions and we present existence results to problem (1.1) in Rn and in an infinite dimensional Hilbert space byreplacing the additional assumptions in [3] and [4] by a weaker and more natural condition.

References[1] F. Ancona; G. Colombo, Existence of solutions for a class of nonconvex differential Inclusions , Rend. Sem. Mat. Univ.

Padova, Vol. 83, 71-76, (1990).

[2] J. P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, (1984).

[3] H. Benabdellah; Sur une classe d’equations differentielles multivoques semi-continue superieurement a valeurs nonconvexes, Seminaire d’Analyse Convexe, Montpellier, Expose No. 6, 1991.

[4] H. Benabdellah; C. Castaing and A. Salvadori Compactness and Discretization Methods for differential Inclusions andEvolution Problems, Atti. Sem. Mat. Univ. Modena, XLV, 9-51, (1997).

[5] M. Bounkhel; Existence Results of Nonconvex Differential Inclusions, J. Portugaliae Mathematica, Vol. 59 (2002), No.3, pp. 283-310.

[6] A. Bressan; A. Cellina; G. Colombo, Upper semicontinuous differential Inclusions without convexity, Proc. Amer. Math.Soc., 106, 771-775, (1989).

Laboratoire de Mathematiques Pures et Appliquees, Jijel University, Algeria, Laboratoire de Mathematiques Pures etAppliquees, Departement de Mathematiques, Jijel University, Algeria, [email protected]


54 Nonlinear Elliptic Problem Related to the Hardy Inequalitywith Singular Term at the BoundaryB.Abdellaoui, K.Biroud, J.Davila and F.Mahmoudi

Let Ω ⊂ RN be a bounded regular domain of RN and 1 < p <∞. The paper is divided in two main parts. In the first partwe prove the following improved Hardy Inequality for convex domains. Namely, for all φ ∈W 1,p

0 (Ω), we have∫Ω

|∇φ|pdx− (p− 1

p)p∫Ω

|φ|p

dpdx ≥ C

∫Ω

|∇φ|p(

log

(D

d

))−pdx,

where d(x) = dist(x, ∂Ω), D > supx∈Ø

d(x) and C is a positive constant depending only on p,N and Ω. The optimality of the

exponent of the logarithmic term is also proved. In the second part we consider the following class of elliptic problem−∆u =

uq

d2in Ω,

u > 0 in Ω,u = 0 on ∂Ω,

where 0 < q ≤ 2∗ − 1. We investigate the question of existence and nonexistence of positive solutions depending on therange of the exponent q.

Boumediene Abdellaoui: Departement de Mathematiques, Universite Abou Bakr Belkaıd, Tlemcen 13000, Algeria,[email protected]

K. Biroud: Departement de Mathematiques, Universite Abou Bakr Belkaıd, Tlemcen 13000, Algeria, kh biroud @ya-hoo.fr

J. Davila: Departamento de Ingenieria Matematica, CMM, Universidad de Chile, Casilla 170-3 Correo 3, Santiago,Chile, [email protected]

F. Mahmoudi: Departamento de Ingenieria Matematica, CMM, Universidad de Chile, Casilla 170-3 Correo 3, Santiago,Chile, [email protected]


55 On Periodic Solutions of Nonlinear Differential Equations inBanach SpacesAbdullah Cavus, Djavvat Khadjiev and Seda Ozturk

Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complexBanach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator Rλ is defined forpoints of the spectrum , some equivalent conditions for compactness of the quasi-resolvent operators Rλ are given. Thenusing these and some results obtained in [1-7], some theorems on existence of periodic solutions to the non-linear equationsΦ(A)x = f(x) are given ,where Φ(A) is a polynomial of A with complex coefficients and f is a continuous mapping of Hinto itself.

References[1] Y.L. Lybich, Introduction to the Theory of Banach Representations of Groups, Birkhauser,Berlin (1988),

[2] J. Andres,B. Krajc, Periodic solutions in a given set of differential systems J. Math.Anal. Appl., 264 (2001) 495-509.

[3] H. Bart, Periodic strongly continuous semigroups, Ann. Mat. Pura. Appl. 115(1977) 311-318.

[4] M. Bartha, Periodic solutions for differential equations with state-dependent delay and positive feedback, NonlinearAnalysis 53 (2003) 839-857.

[5] A. Cavus, D. Khadjiev, M. Kunt ,On periodic one-parameter groups of linear operators in a Banach space and applica-tions, Journal of Inequalities and Applications, 288(2013),1-20.

[6] D. Khadjiev, A.Cavus, Fourier series in Banach spaces, Inverse and Ill-Posed Problems Series, Ill-Posed and Non-ClassicalProblems of Mathematical Physics and Analysis,

[7] D. Khadjiev,The widest continuous integral, J. Math. Anal. Appl., 326 (2007),1101-1115.

Abdullah Cavus: Karadeniz Technical University, Faculty of Science,Department of Mathematics,Trabzon-Turkey, [email protected]

Djavvat Khadjiev: Karadeniz Technical University, Faculty of Science,Department of Mathematics,Trabzon-Turkey,[email protected]

Seda Ozturk: Karadeniz Technical University, Faculty of Science,Department of Mathematics,Trabzon-Turkey, [email protected]


56 Generalized α-ψ-Contractive type M Mappings of IntegralTypeErdal Karapinar, P.Shahi and Kenan Tas

In this talk, we introduce the two classes of generalized α-ψ-contractive type mappings of integral type and to analyze theexistence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude ofrelevant fixed point theorems of the existing literature. Examples are provided to support the results and concepts presentedherein.

References[1] Samet, B, Vetro, C. and Vetro, P., Fixed point theorem for α-ψ contractive type mappings, Nonlinear Anal. 75 (2012)

2154–2165.

[2] Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, FundamentaMathematicae 3 (1922) 133–181.

[3] Ali, M. U. and Kamran, T.: On (α∗, ψ)-contractive multi-valued mappings, Fixed Point Theory Appl., 2013 2013:137doi:10.1186/1687-1812-2013-137.

[4] Berzig, M. and Rus, M., Fixed point theorems for α-contractive mappings of Meir-Keeler type and applications,math.GN/1303.5798.

[5] Jleli, M., Karapinar, E. and Samet, B., Best proximity points for generalized alpha-psi-proximal contractive typemappings, Journal of Applied Mathematics, Article No: 534127 (2013)

[6] Jleli, M., Karapinar, E. and Samet, B., Fixed point results for α− ψλ contractions on gauge spaces and applications,Abstract and Applied Analysis, (2013) Article Id: 730825

[7] Karapinar, E. and Samet, B., Generalized α-ψ-contractive type mappings and related fixed point theorems withapplications, Abstract and Applied Analysis 2012 Article ID 793486, 17 pages doi:10.1155/2012/793486.

[8] Mohammadi, B. Rezapour, S. Shahzad, N.: Some results on fixed points of α-ψ-Ciric generalized multifunctions. FixedPoint Theory Appl., 2013 2013:24 doi:10.1186/1687-1812-2013-24.

[9] Rus, I. A.: Generalized contractions and applications, Cluj University Press, Cluj-Napoca, 2001.

[10] Bianchini R.M., Grandolfi, M.: Transformazioni di tipo contracttivo generalizzato in uno spazio metrico, Atti Acad.Naz. Lincei, VII. Ser., Rend., Cl. Sci. Fis. Mat. Natur. 45 (1968), 212-216.

[11] Proinov, P.D. : A generalization of the Banach contraction principle with high order of convergence of successiveapproximations Nonlinear Analysis (TMA) 67 (2007), 2361-2369.

[12] Proinov, P.D. : New general convergence theory for iterative processes and its applications to Newton Kantorovichtype theorems, J. Complexity 26 (2010), 3-42.

[13] Shahi, P., Kaur, J. and Bhatia, S. S., Fixed point theorems for α-ψ-contractive type mappings of integral type withapplications, accepted for publication in Journal of Nonlinear and Convex Analysis.

[14] Agarwal, R. P., El-Gebeily, M.A. and Regan, D. O’, Generalized contractions in partially ordered metric spaces,Applicable Analysis 87 (2008) 1–8.

[15] Aliouche, A., A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a con-tractive condition of integral type, Journal of Mathematical Analysis and Applications 322, no. 2, (2006), 796–802.

[16] Arandjelovic, I., Kadelburg, Z. and Radenovic, S., Boyd-Wong-type common fixed point results in cone metric spaces,appl. Math. Comput. 217, (2011), 7167–7171.

[17] Berinde, V., Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002.

[18] Berinde, V., Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces,math.FA/1103.5289.

[19] Berinde, V. and Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metricspaces, Nonlinear Analysis 74 (2011) 4889–4897.

Erdal Karapinar: Department of Mathematics, Atilim University 06836, Incek, Ankara, Turkey, [email protected]

P. Shahi: School of Mathematics and Computer Apps, Thapar University, Patiala-147004, Punjab, India, [email protected]

Kenan Tas: Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey, [email protected]


57 Caristi’s Fixed Point Theorem in Fuzzy Metric SpacesHamid Mottaghi Golshan

In the present work, we extend Caristi’s Fixed Point theorem, Ekeland’s variational principle and Takahashi’s maximizationtheorem to fuzzy metric spaces in the sense of George and Veeramani [A. George , P Veeramani, On some results in fuzzymetric spaces, Fuzzy Sets and Systems. 64 (1994) 395-399]. Further, a direct simple proof of the equivalences between thesetheorems is provided.

References[1] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, . Amer. Math. Soc. 215 (1976) 241-251.

[2] A. George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994) 395-399.

[3] I. Ekeland, Remarques sur les problems variationnels 1, C. R. Acad. Sci., Paris Ser. A–B, 275 (1972) 1057-1059.

[4] W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, in: Fixed Point Theoryand Applications, Marseille, 1989, in: Pitman Res. Notes Math. Ser., vol. 252, Longman Sci. Tech., Harlow, 1991, pp.397-406.

Department of Mathematics, Islamic Azad University, Ashtian Branch, Ashtian, Iran, Tel,Fax:+988627222627. [email protected] or [email protected]

This research was partially supported by Islamic Azad University, Ashtian branch.


58 Determination of the Unknown Coefficient in Time Frac-tional Parabolic Equation with Dirichlet Boundary Condi-tionsEbru Ozbilge and Ali Demir

In this talk the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient k(x) in thelinear time fractional parabolic equation Dαt u(x, t) = (k(x)ux)x 0 < α ≤ 1, with Dirichlet boundary conditions u(0, t) =ψ0(t), u(1, t) = ψ1(t) was discussed. By defining the input-output mappings Φ[·] : K → C1[0, T ] and Ψ[·] : K → C1[0, T ] theinverse problem is reduced to the problem of their invertibility. Hence the main purpose of this study is to investigate thedistinguishability of the input-output mappings Φ[·] and Ψ[·]. This work shows that the input-output mappings Φ[·] andΨ[·] have distinguishability property. Moreover, the value k(0) of the unknown diffusion coefficient k(x) at x = 0 and thevalue k(1) of the unknown diffusion coefficient k(x) at x = 1 can be determined explicitly by making use of measured outputdata (boundary observation) k(0)ux(0, t) = f(t) and k(1)ux(1, t) = h(t) respectively, which brings greater restriction on theset of admissible coefficients. It is also shown that the measured output data f(t) and h(t) can be determined analyticallyby a series representation, which implies that the input-output mappings Φ[·] : K → C1[0, T ] and Ψ[·] : K → C1[0, T ] canbe described explicitly.

References[1] J.Canon and Y.Lin, An inverse problem for finding a parameter in a semi-linear heat equation, J. Math. Anal.Appl.,

145 (1990), 470-484,

[2] J.Canon and Y.Lin, Determination of a parameter p(t) in some quasi-linear parabolic differential equations, Inv.Prob.,4 (1998), 35-44, (3-4):235-265,

[3] J.Canon and Y.Lin, Determination of source parameter in parabolic equations, Mechanica, 27 (1992), 85-94,

[4] M.Dehgan, Identification of a time-dependent coefficient in a partial differential equation subject to an extra measure-ment, Numer. Meth. Part. Diff. Eq., 21 (2004), 621-622,

[5] A.Demir and E. Ozbilge, Analysis of a semigroup approach in the inverse problem of identifying an unknown coefficient,Math. Meth. Appl.Sci.,31 (2008),1635-1645,

[6] A.Demir and E.Ozbilge,Semigroup approach for identification of the unknown coefficient in a quasi-linear parabolicequation, Math. Meth. Appl.Sci.,30 (2007), 1283-1294,

[7] A.Demir and A.Hasanov, Identification of the unknown diffusion coefficient in a linear parabolic equation by thesemigroup approach, J. Math. Anal. Appl.,340 (2008),5-15,

[8] A. Fatullayev, Numerical procedure for the simultaneous determination of unknown coefficients in a parabolic equation,Appl.Math.Comp.,164 (2005), 697-705,

[9] V.Isakov, Inverse problems for partial differential equations, Springer-Verlag, 1998,

[10] R.E. Showalter, Monotone operators in Banach Spaces and nonlinear partial differential equations, United States ofAmerica: American Mathematical Society, 1997,

[11] Y.Luchko, Initial boundary value problems for the one dimensional time-fractional diffusion equa-tion,Frac.Calc.Appl.Anal.,15 (2012),141-160.

Ebru Ozbilge: Izmir University of Economics, Department of Mathematics, Faculty of Science and Literature, SakaryaCaddesi, No.156, 35330, Balcova, Izmir, Turkey, [email protected]

Ali Demir: Kocaeli University, Department of Mathematics, Umuttepe, 41380, Izmit, Kocaeli, Turkey, [email protected]

The research was supported by parts by the Scientific and Technical Research Council (TUBITAK) of Turkey and IzmirUniversity of Economics.


59 On p-adic Ising Model with Competing Interactions on theCayley TreeFarrukh Mukhamedov, Hasan Akın and Mutlay Dogan

It is known that the Ising model is one of the most studied models in statistical mechanics. Since, this model is related toa number of outstanding problems in statistical and mathematical physics, and in graph theory. On the other hand, thatmost of modern science is based on mathematical analysis over real and complex numbers. However, it is turned out thatfor exploring complex hierarchical systems it is sometimes more fruitful to use analysis over p-adic numbers and ultrametricspaces. Therefore, in this direction a lot of investigations are devoted to the mathematical physics models over p-adic field.In the present paper, we further develop the theory of statistical mechanics. Namely, we consider p-adic Ising model withcompeting next-nearest-neighbor interactions on the Cayley tree of order two. Note that usual p-adic Ising model on thetree was earlier studied by the first author. A main aim of this work is the establishment of a phase transition phenomenafor the mentioned model. Here the phase transition means the existence of two nontrivial p-adic Gibbs measures. To provethe occurrence of the phase transition we reduce the problem to the existence of at leat two solutions of nonlinear differenceequations.

Farrukh Mukhamedov: Department of Computational & Theoretical Sciences, Faculty of Science, International IslamicUniversity Malaysia, P.O. Box, 141, 25710, Kuantan, Pahang, Malaysia, [email protected], darrukh [email protected]

Hasan Akın: Department of Mathematics, Faculty of Education, Zirve University, Kizilhisar Campus, Gaziantep, 27260,Turkey, [email protected]

Mutlay Dogan: Department of Mathematics, Faculty of Education, Zirve University, Kizilhisar Campus, Gaziantep,27260, Turkey, [email protected]


60 A Spectral Domain Computational Technique Dedicated toFault Detection in Induction MachineA.Medoued, A.Lebaroud, O.Boudebbouz and D.Sayad

This paper presents a computational technique in the spectral domain based on the analysis of three parameters of any signalissued from experimental measurements. This analysis is applied for the purpose of a better detection and characterizationof defects in induction machine. This technique concerns the analysis of the power spectrum signal, the stator current signaldecomposed in terms of the instantaneous phase and instantaneous frequency using Hilbert transform of the current signalabsorbed by the induction machine. The advantage of this technique is that it makes it possible to highlight the defects ofthe machine components independently of the amplitude of the measured signals and regardless of load level.

References[1] G. B. Kliman, W. J. Premerlani, R. A. Koegl, and D. Hoeweler, A new approach to on-line turn fault detection in AC

motors, in Conf. Rec. IEEE, IAS Annu. Meeting, San Diego, CA, (1996), p. 687–693.

[2] Abdesselam Lebaroud, Guy Clerc, Abdelmalek Khezzar, Ammar Bentounsi, Comparison of the Induction MotorsStator Fault Monitoring Methods Based on Current Negative Symmetrical Component, EPE Journal , Vol. 17 , no 1March (2007).

[3] Abdesselam Lebaroud, Guy Clerc, Classification of Induction Machine Faults by Optimal Time–Frequency Represen-tations, IEEE Trans. on Industrial Electronics, vol. 55, no. 12, Dec (2008), p. 4290-4298.

[4] Ibrahim Ali, El Badaoui Mohamed, Guillet Francois, Bonnardot Frederic, A New Bearing Fault Detection Method inInduction Machines Based on Instantaneous Power Factor, IEEE Transactions on Industrial Electronics, Vol 55, No.12, December (2008), p 4252 – 4259.

[5] Zwe-Lee Gaing; Neural Network induction machine Fault classification, IEEE Transactions on Power Delivery, Vol. 19,Issue: 4, (2004), p. 1560–1568.

[6] F. Zidani, M. E. H. Benbouzid, D. Diallo, and M. S. Nait-Said, Induction motor stator faults diagnosis by a currentConcordia pattern-based fuzzy decision system, IEEE Transactions on Energy Conversion, vol. 18, (2003), p. 469-475.

[7] C. Concari, G. Franceschini, C. Tassoni, ”Differential Diagnosis Based on Multivariable Monitoring to Assess InductionMachine Rotor Conditions,” IEEE Trans. on Industrial Electronics, vol. 55, no. 12, Dec (2008), p. 4156-4166.

[8] A. Khezzar, El Kamel Oumaamar, M. Hadjami, M. Boucherma, M. Razik, H. Induction Motor Diagnosis Using LineNeutral Voltage Signatures, IEEE Trans. on Industrial Electronics, vol. 56, no. 11, Nov (2009), p. 4581 - 4591.

[9] P. J Moore, Frequency relaying based on instantaneous frequency measurement, IEEE, Transaction on power delivery,vol. 11, No. 4, (1996).

[10] G. Didier, Modelisation et diagnostic de la machine asynchrone en presence de defaillances, doctoral thesis , France,(2004).

[11] A.Medoued, A.Lebaroud, A.Boukadoum, T.Boukra, G. Clerc, Back Propagation Neural Network for Classification ofInduction Machine Faults, 8th SDEMPED, IEEE Symposium on Diagnostics for Electrical Machines, Power Electronics& Drives September 5-8, 2011, Bologna, Italy, pp 525-528, 2011.

[12] Medoued Ammar, A Lebaroud and D Sayad, Application of Hilbert transform to fault detection in electric machines,Journal advances indifference equations, Springer Open Journal Volume 2013.

A. Medoued, A. Lebaroud, A. Laifa, D. Sayad: Universite du 20 aout 1955-Skikda, Faculte de Technologie, Departementde genie electrique, Alegria, [email protected], [email protected].


61 Some Results on Double Fuzzy Topogenous OrdersVildan Cetkin and Halis Aygun

The first aim of this talk is to introduce the concept of lattice valued double fuzzy topogenous structure. The second is toinvestigate the connections between the double fuzzy topogenous order, double fuzzy topology, double fuzzy interior operatorand also double fuzzy proximity order. So, we have some results on lattice valued double fuzzy topogenous structure.

References[1] S. E. Abbas, A. A. Abd-Allah, Lattice valued double syntopogenous structure, Journal of the Association of Arab

Universities for Basic and Applied Sciences, 10 (2011): 33-41,

[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986): 87-96

[3] G. Birkhoff, Lattice Theory, Ams Providence, 1995,

[4] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968): 182-190,

[5] V. Cetkin and H. Aygun, On (L,M)-Fuzzy Interior Spaces, Advances in Theoretical and Applied Mathematics, 5(2010): 177-195,

[6] V. Cetkin and H. Aygun, Lattice valued double fuzzy preproximity spaces,Computers and Mathematics with Applica-tions, 60 (2010): 849-864,

[7] D. Coker, An Introduction to Fuzzy Subspaces in Intuitionistic Fuzzy Topological Spaces,J. Fuzzy Math. 4 (1996):749-764,

[8] J. G. Garcia, S.E. Rodabaugh, Order-theoretic, topological, categorical redundancides of interval-valued sets, grey sets,vague sets, interval-valued ”intuitionistic” sets, ”intuitionistic” fuzzy sets and topologies, Fuzzy Sets and Systems, 156(2005): 445-484,

[9] U. Hohle, Upper Semicontinuous Fuzzy Sets and Applications, J. Math. Anall. Appl. 78 (1980): 659-673,

[10] U. Hohle and E. P. Klement, Non-Classical Logic and Their Applications to Fuzzy Subsets, Kluwer Academic Publisher,Dordrecht, 1995,

[11] B. Hutton, Normality in Fuzzy Topological Spaces, J. Math. Anal. Appl., 50 (1975): 74-79,

[12] S. Jenei, Structure of Girard Monoids on [0,1] Chapter 10 in: Topological and Algebraic Structures in Fuzzy Sets,S.E.Rodabaugh, E.P.Klement eds., Kluwer Acad. Publ., 2003,

[13] A.K.Katsaras, On fuzzy syntopogenous structures, Rev. Roum. Math. Pure Appl., 30 (1985): 419-431,

[14] T. Kubiak, On Fuzzy Topolgies, Ph.D Thesis, A. Mickiewicz, Poznan (1985),

[15] Y. M. Liu, M. K. Luo, Fuzzy Topology, World Scientific Publishing, Singapore, (1997): 323-336,

[16] S. K. Samanta, T. K. Mondal, On Intuitionistic Gradation of Openness,Fuzzy Sets and Systems, 131 (2002): 323-336,

[17] A. P. Sostak, On a Fuzzy Topological Structure, Suppl. Rend. Circ. Matem. Palermo ser. II, 11 (1985): 89-102.

Vildan Cetkin: Kocaeli University, Faculty of Arts and Science, Department of Mathematics, Umuttepe Campus,Kocaeli-Turkiye, [email protected], [email protected]

Halis Aygun: Kocaeli University, Faculty of Arts and Science, Department of Mathematics, Umuttepe Campus, Kocaeli-Turkiye, [email protected]


62 Finding Fixed Points of Firmly Nonexpansive-Like Mappingsin Banach SpacesFumiaki Kohsaka

We construct a strongly relatively nonexpansive sequence from a given sequence of firmly nonexpansive-like mappings witha common fixed point in Banach spaces. Using this construction, we next obtain two convergence theorems for firmlynonexpansive-like mappings in Banach spaces and discuss their applications to a zero point problem for maximal monotoneoperators and a convex feasibility problem.

Let C be a nonempty subset of a real smooth Banach space X and J : X → X∗ the normalized duality mapping. Amapping T : C → X is said to be firmly nonexpansive-like [2, 4] if

〈Tx− Ty, J(x− Tx)− J(y − Ty)〉 ≥ 0

for all x, y ∈ C.

References[1] K. Aoyama, Y. Kimura, and F. Kohsaka, Strong convergence theorems for strongly relatively nonexpansive sequences

and applications, J. Nonlinear Anal. Optim. 3 (2012), 67–77.

[2] K. Aoyama and F. Kohsaka, Existence of fixed points of firmly nonexpansive-like mappings in Banach spaces, FixedPoint Theory Appl. 2010, Art. ID 512751, 15 pages.

[3] K. Aoyama and F. Kohsaka, Strongly relatively nonexpansive sequences generated by firmly nonexpansive-like mappings,Fixed Point Theory Appl. 2014, 2014: 95, 13 pages.

[4] K. Aoyama, F. Kohsaka, and W. Takahashi, Three generalizations of firmly nonexpansive mappings: Their relationsand continuity properties, J. Nonlinear Convex Anal. 10 (2009), 131–147.

[5] K. Aoyama, F. Kohsaka, and W. Takahashi, Strongly relatively nonexpansive sequences in Banach spaces and appli-cations, J. Fixed Point Theory Appl. 5 (2009), 201–224.

[6] K. Ball, E. A. Carlen, and E. H. Lieb, Sharp uniform convexity and smoothness inequalities for trace norms, Invent.Math. 115 (1994), 463–482.

[7] B. Beauzamy, Introduction to Banach spaces and their geometry, North-Holland Publishing Co., Amsterdam, 1985.

[8] L. M. Bregman, The method of successive projection for finding a common point of convex sets , Soviet Math. Dokl.6 (1965), 688–692.

[9] G. Crombez, Image recovery by convex combinations of projections, J. Math. Anal. Appl. 155 (1991), 413–419.

[10] Y. Kimura and K. Nakajo, The problem of image recovery by the metric projections in Banach spaces, Abstr. Appl.Anal. 2013, Art. ID 817392, 6 pages.

[11] B. Martinet, Determination approchee d’un point fixe d’une application pseudo-contractante. Cas de l’application prox,C. R. Acad. Sci. Paris Ser. A-B 274 (1972), A163–A165.

[12] R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optimization 14 (1976),877–898.

[13] Y. Takahashi, K. Hashimoto, and M. Kato, On sharp uniform convexity, smoothness, and strong type, cotype inequal-ities, J. Nonlinear Convex Anal. 3 (2002), 267–281.

Department of Computer Science and Intelligent Systems, Oita University, Japan, [email protected]


63 A Fourth Order Accurate Approximation of the First andPure Second Derivatives of the Laplace Equation on a Rect-angleA.A.Dosiyev and H.M.Sadeghi

In this talk, we discuss an approximation of the first and pure second order derivatives of a solution of the Dirichlet problemon a rectangular domain. The boundary values on the sides of the rectangle are supposed to have the sixth derivativessatisfying the Holder condition. On the vertices, besides the continuity condition, the compatibility conditions, which resultfrom the Laplace equation for the second and fourth derivatives of the boundary values, given on the adjacent sides, arealso satisfied. Under these conditions uniform approximation of order O(h4) (h is the grid size), is obtained for the solutionof the Dirichlet problem on a square grid, its first and pure second derivatives, by a simple difference schemes.

A. A. Dosiyev: Eastern Mediterranean University, Department of Mathematics, Gazimagusa, Cyprus, Mersin 10, Turkey,[email protected]

H. M. Sadeghi: Eastern Mediterranean University, Department of Mathematics, Gazimagusa, Cyprus, Mersin 10,Turkey, [email protected]


64 On the Positive Solutions for the Boundary Value Problemsat ResonanceUmmahan Akcan and Nuket Aykut Hamal

In this study, we investigate the existence of two positive concave solutions to the second-order three-point boundary value

problems with integral boundary conditions, u′′

(x)+f(x, u(x)) = 0, u′(0) = u(0), u(1) = α

∫ η

0u(s)ds, where 0 < η < 1 and

f ∈ C((0, 1)× [0,+∞), [0,+∞)). The interesting point here is that we consider the BVP to the resonance case αη(2 +η) = 4to find a new existence result. The proof is based upon the Monoton Iterative Technique.

References[1] H. Liu, Z. Ouyang, Existence of solutions for second-order three-point integral boundary value problems at resonance,

Boundary Value problem., (2013):197 doi:10.1186/1687-2770-2013-197.

[3] J. J. Nieto, Existence of a solution for a three-point boundary value problem for a second-order differential equation atresonance, Boundary Value Problem., (2013):130 doi:10.1186/1687-2770-2013-130,

[4] A. Boucherif, Second-order boundary value problems with integral boundary conditions, Nonlinear Anal., 70 (2009)364-371,

[5] T. Jankowski, Differantial equations with integral boundary conditions, Journal of Computational and Applied Mathe-matics, 147 (2002) 1-8,

[6] X. Zhang, Existence and iteration of monotone positive solutions for an elastic beam equation with a corner, NonlinearAnalysis: Real World Applications, 10 (2009) 2097-2103,

[7] H. Pang, M. Feng, W. Ge, Existence and monotone iteration of positive solutions for a three-point boundary valueproblem, Applied Mathematics Letters, 21 (2008) 656-661,

[8] Q. Yao, Successive Iteration and Positive Solutions for Nonlinear Second-Order Three-Point Boundary Value Problems,Computer and Mathematics with Applications, 50 (2005) 433-444,

Ummahan Akcan: Anadolu University, Faculty of Science, Department of Mathematics, Eskisehir-Turkey, [email protected]

Nuket Aykut Hamal: Ege University, Faculty of Science, Department of Mathematics, Izmir-Turkey, [email protected]


65 On Weighted Approximation of Multidimensional SingularIntegralsGumrah Uysal and Ertan Ibikli

In this talk, we give some theorems about pointwise approximation to the functions belong to weighted Lebesgue spaceL1,w(Rn), by family of convolution type singular integral operators. Moreover, we will verify the theoretical results withsome graphical illustrations.

References[1] R. Taberski, Singular integrals depending on two parameters, Rocznicki Polskiego towarzystwa matematycznego, Seria

I. Prace matematyczne, VII (1962), pp.173–179.

[2] A.D. Gadjiev , On convergence of integral operators depending on two parameters, Dokl. Acad. Nauk. Azerb. SSR, XIX(1963) No. 12, pp. 3–7.

[3] A.D. Gadjiev, On the order of convergence of singular integrals depending on two parameters, Special questions offunctional analysis and its applications to the theory of differential equations and functions theory, Baku, (1968), pp.40-44.

[4] P.L. Butzer and R.J.Nessel , Fourier Analysis and Approximation, Academic Press, New York, London, (1971).

[5] H. Karslı and E. Ibikli, On convergence of convolution type singular integral operators depending on two parameters,Fasc. Math., no.38, (2007), pp.25-39.

[6] G. Folland, Real Analysis: Modern Techniques, John Wiley & Sons, Second Edition, (1999).

[7] G.A. Anastassiou and S.G. Gal, Approximation Theory: Moduli of Continuity and Global Smoothness Preservation.Birkhauser, Boston, (2000).

[8] S.E. Almali, Approximation of non-convolution type of integral operators at Lebesgue point for non-integrable of func-tion, International Congress On Computational and Applied Maths., Ghent, Belgium, (2012), pp. 27.

Gumrah Uysal: Karabuk University, Faculty of Science, Department of Mathematics, Balıklarkayası Mevkii, Karabuk,Turkey, [email protected]

Ertan Ibikli: Ankara University, Faculty of Science, Department of Mathematics, Tandogan, Ankara, Turkey, [email protected]


66 On Hermite-Hadamard Type Inequalities for ϕ−Convex Func-tions via Fractional IntegralsMehmet Zeki Sarıkaya and Hatice Yaldız

In this talk, we establish integral inequalities of Hermite-Hadamard type involving Riemann-Liouville fractional integrals forϕ-convex functions and some new inequalities of right-hand side of Hermite-Hadamard type are given for functions whosefirst derivatives absolute values ϕ−convex functions via Riemann-Liouville fractional integrals.

References[1] A.G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.

[2] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) (2009),Art. 86.

[3] Z. Dahmani, New inequalities in fractional integrals, International Journal of Nonlinear Scinece, 9(4) (2010), 493-497.

[4] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal.1(1) (2010), 51-58.

[5] Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonl. Sci. Lett. A, 1(2) (2010), 155-160.

[6] Z. Dahmani, L. Tabharit, S. Taf, New generalizations of Gruss inequality usin Riemann-Liouville fractional integrals,Bull. Math. Anal. Appl., 2(3) (2010), 93-99.

[7] S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIAMonographs, Victoria University, 2000.

[8] S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means ofreal numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.

[9] R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag,Wien (1997), 223-276.

[10] S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley& Sons, USA, 1993, p.2.

[11] J.E. Pecaric, F. Proschan and Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, AcademicPress, Boston, 1992.

[12] M.Z. Sarikaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstract and Ap-plied Analysis, Volume 2012 (2012), Article ID 428983, 10 pages.

[13] M. Z. Sarikaya, M. Buyukeken and M. E. Kiris, On some generalized integral inequalities for ϕ-convex functions,Studia Universitatis Babes-Bolyai Mathematica, (2014)accepted.

[14] M.Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard’s inequalities for fractional integrals and relatedfractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048, 57 (2013) 2403–2407.

[15] M. Tunc, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27:4 (2013),559–565.

[16] E. A. Youness, E-convex sets, E-convex functions and E-convex programming, J. of Optim. Theory and Appl., 102,No. 2 (1999), 439-450.

Duzce University, Faculty of Science and Arts, Department of Mathematics, Duzce-Turkiye, [email protected],[email protected]


67 Behavior of Positive Solutions of a Multiplicative DifferenceEquationDurhasan Turgut Tollu, Yasin Yazlık and Necati Taskara

In this talk, we deal with the positive solutions of the multiplicative difference equation

yn+1 =ayn−1

bynyn−1 + cyn−1yn−2 + d, n ∈ N0,

where the coefficients a, b, c, d are positive real numbers and the initial conditions y−2, y−1, y0 are nonnegative realnumbers. Here, we investigate global character, periodicity, boundedness and oscillation of positive solutions of the aboveequation.

References[1] E. Camouzis and G. Ladas. Dynamics of Third-order Rational Difference Equations with Open Problems and Con-

jectures, Volume 5 of Advances in Discrete Mathematics and Applications, Chapman & Hall/CRC, Boca Raton, FL,2008.

[2] C. Cinar, On the positive solutions of the difference equation xn+1 =xn−1

1+xnxn−1, Applied Mathematics and Compu-

tation, 150 (2004), 21-24.

[3] S. Stevic, More on a rational recurrence relation, Appl. Math. E-Notes 4 (2004), 80-85.

[4] A. Andruch-Sobilo, M. Migda, Further properties of the rational recursive sequence xn+1 =axn−1

b+cxnxn−1, Opuscula

Mathematica 26(3)(2006) 387- 394.

[5] I. Bajo, E. Liz, Global behaviour of a second-order nonlinear difference equation, J. Differ. Equations Appl. 17 (10)(2011), 1471-1486.

[6] S. Stevic, On the difference equation xn =xn−k

b+cxn−1···xn−k, Applied Mathematics and Computation 218 (2012), 6291-

6296.

[7] R. Abu-Saris, C. Cinar, I. Yalcinkaya, On the asymptotic stability of xn+1 =a+xnxn−kxn+xn−k

, Computers & Mathematics

with Applications, 56(5) (2008)1172-1175.

[8] H.M. El-Owaidy, A.M. Ahmet, A.M. Youssef, On the dynamics of the recursive sequence xn+1 =αxn−1

β+γxpn−2

, Applied

Mathematics Letters, 18 (9)(2005), 1013-1018.

[9] R. Karatas, Global behaviour of a higher order difference equation, Computers & Mathematics with Applications 60(2010), 830-839.

[10] M. A. Obaid, E. M. Elsayed and M. M. El-Dessoky, Global Attractivity and Periodic Character of Difference Equationof Order Four, Discrete Dynamics in Nature and Society, (2012), Article ID:746738.

[11] M. E. Erdogan, Cengiz Cinar, Ibrahim Yalcinkaya, On the dynamics of the recursive sequence xn+1 =αxn−1

β+γx2n−2xn−4+γxn−2x2n−4

, Computers & Mathematics with Applications, 61 (2011), 533-537.

[12] Y. Yazlik, On the solutions and behavior of rational difference equations, Journal of Computational Analysis andApplications, 17(3)(2014), 584-594.

[13] T.F. Ibrahim, On the third order rational difference equation xn+1 =xnxn−2

xn−1(a+bxnxn−2), Int. J. Contemp. Math.

Sciences 4(27)(2009), 1321-1334.

[14] X. Yang, W. Su, B. Chen, G. M. Megson, and D. J. Evans, On the recursive sequence xn+1 =axn−1+bxn−2

c+dxn−1xn−2, Applied

Mathematics and Computation, 162 (2005) 1485–1497.

[15] H. El-Metwally, E. M. Elsayed, Qualitative study of solutions of some difference equations, Abstract and AppliedAnalysis, Article ID 248291, (2012), 16 pages.

[16] D. Simsek, C. Cinar and I. Yalcinkaya, On the recursive sequence xn+1 =xn−(5k+9)

1+xn−4xn−9...xn−(5k+4), Taiwanese Journal

of Mathematics 12(5)(2008), 1087-1099.

[17] D. T. Tollu, Y. Yazlik, N. Taskara, On the Solutions of two special types of Riccati Difference Equation via FibonacciNumbers, Advances in Difference Equations, 2013, 2013:174.

Durhasan Turgut Tollu: Department of Mathematics-Computer Sciences, Faculty of Science, Necmettin Erbakan Uni-versity, 42090, Konya-Turkiye, [email protected]

Yasin Yazlik: Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, 50300Nevsehir-Turkiye, [email protected]

Necati Taskara: Department of Mathematics, Faculty of Science, Selcuk University, Campus, 42075, Konya- Turkiye,[email protected]


68 A New Generalization of the Midpoint Formula for n−TimeDifferentiable Mappings which are ConvexCetin Yıldız and M.Emin Ozdemir

Let f : I ⊂ R → R be a convex mapping defined on the interval I of real numbers and a, b ∈ I, with a < b. The followingdouble inequality is well known in the literature as the Hermite-Hadamard inequality:

f

(a+ b

2

)≤

1

b− a

∫ b

af(x)dx ≤

f(a) + f(b)

2.

A function f : [a, b] ⊂ R→ R is said to be convex if whenever x, y ∈ [a, b] and t ∈ [0, 1], the following inequality holds:

f(tx+ (1− t)y) ≤ tf(x) + (1− t)f(y).

In this paper, a new identity for n−time differentiable functions is established and by using the obtained identity, somenew inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex andconcave functions.

References[1] M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second

derivatives absolute values are quasi-convex. Tamkang Journal of Mathematics, 41(4), 2010, 353-359.

[2] S.-P. Bai, S.-H. Wang and F. Qi, Some Hermite-Hadamard type inequalities for n-time differentiable (α,m)-convexfunctions, Jour. of Ineq. and Appl., 2012, 2012:267.

[3] P. Cerone, S.S. Dragomir and J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings andapplications, Demonstratio Math., 32 (4) (1999), 697-712.

[4] P. Cerone, S.S. Dragomir and J. Roumeliotis and J. Sunde, A new generalization of the trapezoid formula for n-timedifferentiable mappings and applications, Demonstratio Math., 33 (4) (2000), 719-736.

[5] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Mono-graphs, Victoria University, 2000. Online:[http://www.staxo.vu.edu.au/RGMIA/monographs/hermite hadamard.html].

[6] D.-Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. Jour., 43 (2003),335-343.

[7] J. L. W. V. Jensen, On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B., 16, 49-69, 1905.

[8] W.-D. Jiang, D.-W. Niu, Y. Hua and F. Qi, Generalizations of Hermite-Hadamard inequality to n-time differentiablefunction which are s-convex in the second sense, Analysis (Munich), 32 (2012), 209-220

[9] M.E. Ozdemir, C. Yıldız, New Inequalities for n-time differentiable functions, Arxiv:1402.4959v1.

Cetin Yıldız: Ataturk University, K. K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum-Turkey, [email protected]

M. Emin Ozdemir: Ataturk University, K. K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum-Turkey, [email protected]


69 Global Bifurcations of Limit Cycles in the Classical LorenzSystemValery Gaiko

We consider a three-dimensional polynomial dynamical system

x = σ(y − x), y = x(r − z)− y, z = xy − bz (69.1)

known as the Lorenz system. Historically, (69.1) was the first dynamical system for which the existence of an irregularattractor (chaos) was proved for σ = 10, b = 8/3, and 24,06 < r < 28. The Lorenz system (69.1) is dissipative and symmetricwith respect to the z-axis. The origin O(0, 0, 0) is a singular point of system (69.1) for any σ, b, and r. It is a stable nodefor r < 1. For r = 1, the origin becomes a triple singular point, and then, for r > 1, there are two more singular points inthe system: O1(

√b(r − 1),

√b(r − 1), r − 1) and O2(−

√b(r − 1),−

√b(r − 1), r − 1) which are stable up to the parameter

value ra = σ(σ + b+ 3)/(σ − b− 1) (ra ≈ 24,74 for σ = 10 and b = 8/3). For all r > 1, the point O is a saddle-node.For many years, the Lorenz system (69.1) has been the subject of study by numerous authors; see, e. g., [1]–[5]. However,

until now the structure of the Lorenz attractor is not clear completely yet, and the most important question at present is tounderstand the bifurcation scenario of chaos transition in system (69.1) which is related to Smale’s Fourteenth Problem [4].In this talk, we present a new bifurcation scenario for system (69.1), where σ = 10, b = 8/3, and r > 0, using numericalresults of [5] and a bifurcational geometric approach to the global qualitative analysis of three-dimensional dynamicalsystems which was applied earlier in the two-dimensional case [6]–[8]. This scenario connects globally the homoclinic,period-doubling, Andronov–Shilnikov, and period-halving bifurcations of limit cycles in the Lorenz system (69.1) [9].

References[1] Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, 2004.

[2] N. A Magnitskii, S. V. Sidorov, New Methods for Chaotic Dynamics, World Scientific, New Jersey, 2006.

[3] L. P. Shilnikov et al., Methods of Qualitative Theory in Nonlinear Dynamics. I, II, World Scientific, New Jersey, 1998,2001.

[4] S. Smale, Mathematical problems for the next century, Math. Intelligencer, 20 (1998), 7–15.

[5] C. Sparrou, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer, New York, 1982.

[6] V. A. Gaiko, Global Bifurcation Theory and Hilbert’s Sixteenth Problem, Kluwer, Boston, 2003.

[7] V. A. Gaiko, On limit cycles surrounding a singular point, Differ. Equ. Dyn. Syst., 20 (2012), 329–337.

[8] V. A. Gaiko, The applied geometry of a general Lienard polynomial system, Appl. Math. Letters, 25 (2012), 2327–2331.

[9] V. A. Gaiko, Chaos transition in the Lorenz system, Herald Odesa Nation. Univ. Ser. Math. Mech., 18 (2013), 51–58.

United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus, [email protected]


70 Curvature of Curves Parameterized by a Time ScaleSibel Pasalı Atmaca and Omer Akguller

Geometric aspect of the theory of time scales is extensively studied afterwards the introduction of partial derivatives ontime scales. However, an intrinsic characteristic such as curvature of a curve parameterized by a time scale is still an openquestion. In this talk, we present the concept of curvature via symmetric derivative on time scales. This approach involvesboth characteristics of discrete and classical differential geometry, and accurately applicable to globally discrete settings.By the help of this definition of curvature, we also present the bending energy for a curve parameterized by a time scale.

References[11] A.M.C. Brito Da Cruz,N. Martins,D.F.M. Torres, Symmetric differentiation on time scales, Applied Mathematics

Letters 26 (2), (2013), pp. 264-269.

[6] C. Dinu, Diamond-α tangent lines of time scales parametrized regular curves, Carpathian Journal of Mathematics, 25(1), (2009), pp. 55-60.

[8] D. Ucar, M.S. Seyyidoglu, Y. Tuncer,M.K. Berktas, V.F. Hatipoglu, V.F., Forward curvatures on time scales, Abstractand Applied Analysis, (2011) , art. no. 805948.

[3] E. Ozyılmaz, Directional derivative of vector field and regular curves on time scales, Applied Mathematics and Me-chanics (English Edition), 27 (10), (2006), pp. 1349-1360.

[2] G. Guseinov, E. Ozyılmaz, Tangent lines of generalized regular curves parametrized by time scales , Turkish Journalof Mathematics, 25 (4), (2001), pp. 553-562.

[9] J.L. Cieslinski, Pseudospherical surfaces on time scales: A geometric definition and the spectral approach, Journal ofPhysics A: Mathematical and Theoretical, 40 (42), (2007), pp. 12525-12538.

[1] M. Bohner, G. Guseinov, Partial differentiation on time scales, Dynamic Systems and Applications, 13, (2004), 351-379.

[10] M. Bohner, G. Guseinov, Surface areas and surface integrals on time scales, Dynamic Systems and Applications, 19(3-4), (2010), pp. 435-454.

[4] S. P. Atmaca, Normal and osculating planes of ∆-regular curves, Abstract and Applied Analysis, (2010) , art. no.923916.

[5] S. P. Atmaca, O. Akguller, Surfaces on time scales and their metric properties, Advances in Difference Equations,(2013), Volume 2013, June 2013, Article number 170.

[7] S. P. Atmaca, O. Akguller, The time scale calculus approach to the geodesic problem in 3D dynamic data sets,Mathematical and Computational Applications, 18 (3), (2013), pp. 421-427.

Sibel Pasalı Atmaca: Mugla Sıtkı Kocman University, Faculty of Science, Department of Mathematics, Mentese, Mugla-Turkiye, [email protected]

Omer Akguller: Mugla Sıtkı Kocman University, Faculty of Science, Department of Mathematics, Mentese, Mugla-Turkiye, [email protected]


71 Essential Norms of Products of Weighted Composition Oper-ators and Differentiation Operators Between Banach Spacesof Analytic FunctionsJasbir S.Manhas and Ruhan Zhao

We obtain several estimates of the essential norms of the products of differentiation operators and weighted compositionoperators between weighted Banach spaces of analytic functions with general weights.

Jasbir S. Manhas: Sultan Qaboos University, Department of Mathematics & Statistics, Muscat, Oman, [email protected]

Ruhan Zhao: State University of New York (SUNY), Department of Mathematics, Brockport, U.S.A., [email protected]


72 On the Null Forms, Integrating Factors and First Integralsto Path EquationsIlker Burak Giresunlu and Emrullah Yasar

In this work, we consider the path equation

y′′ −f ′(y)

f(y)(y′)2 −

f ′(y)

f(y)= 0

which modeling the drag forces [1]. The drag forces are the major source of energy loss for objects moving in a fluid medium.Using the relationship between semi-algorithmic Prelle-Singer method [6] and λ-symmetry approach [6], we obtained null-forms, integrating factors, first integrals and general solutions [4]. Nevertheless exploiting the Lie-point type symmetries weconstructed systematically the Jacobi Last Multiplier’s (JLM) [5]. After yielding the these multipliers we obtained Darbouxpolynomials of the under considered equation.The results was tabulated and compared with those gained by the other methods [6, 7].

References[1] M. Pakdemirli, The drag work minimization path for a flying object with altitude-dependent drag parametres, Pro-

ceedings of the Institution of Mechanical Engineers C, Journal of Mechanical Engineering Science, 223(5) (2009),1113-1116,

[2] V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, On the complete integrability and linearization of certainsecond-order nonlinear ordinary differential equations, Proc. R. Soc. A., 461 (2005), 2451-2477.

[3] C. Muriel and J. L. Romero, Integrating Factors and λ-Symmetries, JNMP, 15 (2008), 300-309,

[4] R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, Interplay of symmetries, null forms,Darboux polynomials, integrating factors and Jacobi multipliers in integrable second order differential equations, Proc.R. Soc. A, 470 (2014),

[5] M. Nucci, Jacobi last multiplier and Lie symmetries: a novel application of an old relationship, J. Nonlinear Math.Phys., 12 (2005), 284-304,

[6] M. Pakdemirli and Y. Aksoy, Group classification for path equation describing minimum drag work and symmetryreductions, Applied Mathematics and Mechanics (English Edition), 31(7) (2010), 911-916,

[7] G. Gun and T. Ozer, First Integrals, Integrating Factors, and Invariant Solutions of the Path Equation Based on Noetherand λ-Symmetries, Abstract and Applied Analysis, 15 (2013).

Uludag University, Faculty of Arts and Science, Department of Mathematics, Gorukle, Bursa-Turkiye, [email protected], [email protected]


73 Commutativity of Lommel and Halm Differential EquationsMehmet Emir Koksal

Many engineering systems are composed of cascade connection of subsystems of simple orders. This is very important indesign of electrical and electronic systems. Hence, the commutativity, which is the functional invariance under the changeof the connection order, is very important from the practical point of view.

This presentation introduces the commutativity of systems defined by Lommel and Halm type differential equations.These differential equations have been described in the literature and they represents some particular physical systems. Theexplicate requirements for commutativity of these systems are derived. Under certain circumstances, these systems havecommutative pairs some of which have explicit analytical solutions. The outcomes of the presentation is expected to leadnew design trends in engineering as to improve the total system performance covering sensitivity, stability, disturbance androbustness.

References[1] E. Marshall, Commutativity of time varying systems. Electronic Letters, 18 (1977), 539-540.

[2] M. Koksal, Commutativity of second order time-varying systems, Int. J. of Cont., 3 (1982), 541-544,

[3] M. Koksal, Commutativity of 4th order systems and Euler systems, Proceeding of National Congress of ElectricalEngineers (in Turkish), Paper no:BI-6, Adana, Turkey, 1985,

[4] M. Koksal and M. E. Koksal, Commutativity of linear time-varying differential systems with non-zero initial conditions:a review and some new extensions, Mathematical Problems in Engineering, 2011 (2011), 1-25,

[5] M. E. Koksal, The Second Order Commutative Pairs of a First Order Linear Time-Varying System, Applied Mathematicsand Information Sciences, 9 (2015), 1-6.

Mevlana University, Department of Primary Mathematics Education, 42003 Selcuklu, Konya, Turkey, [email protected]


74 Equivalence Between Some Iterations in CAT (0) SpacesKyung Soo Kim

In this talk, we obtain some equivalence conditions for the convergence of iterative sequences for set-valued contractionmapping in CAT (0) spaces are obtained.

References[1] M. Bridson and A. Haefliger, Metric spaces of Non-Positive Curvature, Springer-Verlag, Berlin, Heidelberg, 1999.

[2] F. Bruhat and J. Tits, Groups reductifss sur un corps local. I. Donnees radicielles valuees, Publ. Math. Inst. Hautes

Etudes Sci., 41 (1972), 5–251.

[3] P. Chaoha and A. Phon-on, A note on fixed point sets in CAT (0) spaces, J. Math. Anal. Appl., 320 (2006), 983–987.

[4] S. Dhompongsa and B. Panyanak, On triangle-convergence theorems in CAT (0) spaces, Comput. Math. Anal., 56(2008), 2572–2579.

[5] J.C. Dunn, Iterative construction of fixed points for multivalued operators of the monotone type, J. Funct. Anal., 27(1)(1978), 38–50.

[6] R. Espınola and B. Piatek, The fixed point property and unbounded sets in CAT (0) spaces, J. Math. Anal. Appl., 408(2013), 638–654.

[7] S. Ishikawa, Fixed point by a new iteration, Proc. Amer. Math. Soc., 44 (1974), 147–150.

[8] M.A. Khamsi and W.A. Kirk, On uniformly Lipschitzian multivalued mappings in Banach and metric spaces, NonlinearAnal., 72 (2010), 2080–2085.

[9] J.K. Kim, K.S. Kim and Y.M. Nam, Convergence and stability of iterative processes for a pair of simultaneouslyasymptotically quasi-nonexpansive type mappings in convex metric spaces, J. of Compu. Anal. Appl., 9(2) (2007),159–172.

[10] W.A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68(12) (2008), 3689–3696.

[11] L. Leustean, A quadratic rate of asymptotic regularity for CAT (0)-spaces, J. Math. Anal. Appl., 325 (2007), 386–399.

[12] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506–510.

[13] S.B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–488.

[14] E. Picard, Sur les groupes de transformation des equations differentielles lineaires, Comptes Rendus Acad. Sci. Paris,96 (1883), 1131–1134.

[15] S. Saejung, Halpern’s iteration in CAT (0) spaces, Fixed Point Theory Appl., 2010, Article ID 471781, 13 pages.

Kyungnam University, Department of Education, Mathematics Education Major, Changwon, Gyeongnam, 631-701,Korea, [email protected]

This research was supported by Basic Science Research Program through the National Research Foundation of Ko-rea(NRF) funded by the Ministry of Education(2012R1A1A4A01010526)


75 On Certain Combinatoric Convolution Sums of Divisor Func-tionsDaeyeoul Kim and Nazli Yildiz Ikikardes

In this talk, we study certain combinatorial convolution sums involving divisor functions and their relations to Bernoullipolynomials. We establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived fromBernoulli polynomials.

References[1] D. Kim and A. Bayad, Convolution identities for twisted Eisenstein series and twisted divisor functions, Fixed Point

Theory and Applications, 2013, 81,

[2] D. Kim and N.Y. Ikikardes, Certain combinatoric Bernoulli polynomials and convolution sums of divisor functions,Advance Difference Equations, 2013, 2013:310, 11pp.,

[3] K. S. Williams, Number Theory in the Spirit of Liouville, London Mathematical Society, Student Texts 76, Cambridge,2011.

Daeyeoul Kim: National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811,South Korea, [email protected]

Nazli Yildiz Ikikardes: Department of Elementary Mathematics Education, Necatibey Faculty of Education, BalikesirUniversity, 10100 Balikesir, Turkey, [email protected]


76 Some Properties of the Genocchi Polynomials with the Vari-able [x]qJ.Y.Kang and C.S.Ryoo

We introduce the Genocchi polynomials with the variable [x]q and we get some relations of their polynomials by the p-adicintegral on Zp. We also observe an interesting phenomenon of scattering of the zeros of the Genocchi polynomials with thevariable [x]q in comlex plane.

References[1] Cangul, I. N., Ozden, H., Simsek, Y., A new approach to q-Genocchi numbers and their interpolation functions,

Nonlinear Analysis Series A: Theory, Methods and Applications, 71 2009, 793-799.

[2] B. Kupershmidt, Reflection symmetries of q-Bernoulli polynomials, J. Nonlinear Math. Phys., 12 (2005), suppl. 1,412-422.

[3] D. S. Kim, T. Kim, Y. H. Kim, S. H. Lee, Some arithmetic properties of Bernoulli and Euler numbers, Adv. Stud.Contemp. Math., 22 (4) (2012), 467-480.

[4] Veli Kurt and Mehmet Cenkci, A nes approach to q-Genocchi numbers and polynomials, Bull. Korean Math. Soc., 47(3) (2010), 575-583.

[5] Min-Soo Kim, On Euler numbers, polynomials and related p-adic integrals, Journal of Number Theory, 129 (2009),2166-2179.

[6] T. Kim, q-Volkenborn integration, Russian Journal of Mathematical Physics, 9 (2002) ,288-299.

[7] T. Kim, On the q-extension of Euler and Genocchi numbers, Journal of Mathematical Analysis and Applications, 326(2007), 1458-1465.

[8] T. Kim, An invariant p-adic q-integrals on Zp, Applied Mathematics Letters, 21 (2008), 105-108.

[9] S. H. Rim, K. H. Park and E. J. Moon, On Genocchi Numbers and Polynomials, Abstract and Applied Analysis, 2008,Article ID 898471, 7 pages.

[10] C. S. Ryoo, A numerical computation on the structure of the roots of q-extension of Genocchi polynomials, AppliedMathematics Letters, 21 (4) (2008), 348-354.

[11] Y. Simsek, I. N. Cangul, V. Kurt and D. Kim, q-Genocchi numbers and polynomials associated with q-Genocchi-typeL-Functions, Advances in Difference Equations, (2008), Article ID: 815750, 12 pages.

J.Y. Kang: Department of Mathematics, Hannam University, Daejeon 306-791, Korea, [email protected]. Ryoo: Department of Mathematics, Hannam University, Daejeon 306-791, Korea, [email protected] work was supported by NRF(National Research Foundation of Korea) Grant funded by the Korean Government

(NRF-2013-Fostering Core Leaders of the Future Basic Science Program).


77 Boundedness of Localization Operators on Lorentz MixedNormed Modulation SpacesAyse Sandıkcı

The localization operator Aϕ1,ϕ2a with symbol a ∈ S′

(Rd)

and windows ϕ1, ϕ2 is defined to be

Aϕ1,ϕ2a f (t) =

∫R2d

a (x,w)Vϕ1f (x,w)MwTxϕ2dxdw.

In this work we study certain boundedness properties for localization operators on Lorentz mixed normed modulation spaces,when the operator symbols belong to appropriate Wiener amalgam spaces and Lorentz spaces with mixed norms.

Some key references are given below.

References[1] P. Boggiatto, Localization operators with Lp symbols on the modulation spaces, In Advances in Pseudo-Differential

Operators, vol. 155 of Oper. Theory Adv. Appl., 149–163, Birkhauser, Basel, 2004.

[2] E. Cordero, K. Grochenig, Time-frequency analysis of localization operators, J. Funct. Anal., 205(1) (2003) , 107-131.

[3] H.G. Feichtinger, F. Luef, Wiener amalgam spaces for the Fundamental Identity of Gabor Analysis, Collect. Math.,Vol.57 No.Extra Volume (2006), 233–253.

[4] D.L. Fernandez, Lorentz spaces, with mixed norms, J. Funct. Anal., 25 (1977) , 128-146.

[5] A.T. Gurkanlı, Time-frequency analysis and multipliers of the spaces M (p, q)(Rd)

and S (p, q)(Rd), J. Math. Kyoto

Univ., 46-3 (2006), 595-616.

[6] K. Grochenig, Foundation of Time-Frequency Analysis. Birkhauser, Boston 2001, ISBN 0-8176-4022-3.

[7] R.A. Hunt, On L (p, q) spaces, Extrait de L’Enseignement Mathematique, T.XII, fasc.4 (1966) , 249-276.

[8] A. Sandıkcı, On Lorentz mixed normed modulation spaces, J. Pseudo-Differ. Oper. Appl., 3 (2012) , 263-281.

[9] A. Sandıkcı, A.T. Gurkanlı, Gabor Analysis of the spaces M (p, q, w)(Rd)

and S (p, q, r, w, ω)(Rd), Acta Math. Sci.,

31B (2011) , 141-158.

[10] A. Sandıkcı, A.T. Gurkanlı, Generalized Sobolev-Shubin spaces, boundedness and Schatten class properties of Toeplitzoperators, Turk J. Math., 37 (2013) , 676-692.

[11] A. Sandıkcı, Continuity of Wigner-type operators on Lorentz spaces and Lorentz mixed normed modulation spaces,Turk J. Math., 38 (2014) , 728-745.

Ondokuz Mayıs University, Faculty of Arts and Science, Department of Mathematics, Atakum, Samsun-Turkey, [email protected]


78 p−Summable Sequence Spaces with Inner ProductsSukran Konca, Hendra Gunawan and Mochammad Idris

We revisit the space `p of p-summable sequences of real numbers. In particular, we show that this space is actuallycontained in a (weighted) inner product space. The relationship between `p and the (weighted) inner product space thatcontains `p is studied. For p > 2, we also obtain a result which describe how the weighted inner product space is associatedto the weights.

References[1] S.K. Berberian, Introduction to Hilbert Space, Oxford University Press, New York, 1961.

[2] H. Gunawan, W. Setya-Budhi, Mashadi, S. Gemawati, On volumes of n-dimensional parallelepipeds on `p spaces,Univerzitet u Beogradu. Publikacije Elektrotehnickog Fakulteta. Serija Matematika, 16 (2005): 48–54.

[3] D. Hilbert, Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen, Reprinted 1953, New York, Chelsea,1912.

[4] M. Idris, S. Ekariani, H. Gunawan, On the space of p-summable sequences, Matematiqki Vesnik. 65 (2013), (1): 58–63.

[5] E. Kreyszig, Introductory Functional Analysis with Applications, New York, John Wiley & Sons, 1978.

[6] P.M. Milicic, Une generalisation naturelle du produit scaleaire dans un espace norme et son utilisation, Univerzitet uBeogradu. Publikacije Elektrotehnickog Fakulteta. Serija Matematika (Beograd), 42 (1987), (56): 63–70.

Sukran Konca: Sakarya University, Faculty of Science, Department of Mathematics, 54187, Sakarya-Turkey, Bitlis ErenUniversity, Department of Mathematics, 13000, Bitlis-Turkey, [email protected] and [email protected]

Hendra Gunawan: Institute of Technology Bandung, Department of Mathematics, 40132, Bandung-Indonesia, [email protected]

Mochammad Idris: Institute of Technology Bandung, Department of Mathematics, 40132, Bandung-Indonesia, LambungMangkurat University, Department of Mathematics, 70711, Banjarbaru-Indonesia [email protected]


79 An Alternative Proof of a Tauberian Theorem for Abel Summa-bility MethodIbrahim Canak and Umit Totur

Using a corollary to Karamata’s main theorem [Math. Z. 32 (1930), 319–320], we prove that if a slowly decreasing sequenceof real numbers is Abel summable, then it is convergent in the ordinary sense.

References[1] R. Schmidt, Uber divergente Folgen und lineare Mittelbildungen, Math. Z., 22 (1925), 89–152,

[2] I. J. Maddox, A Tauberian theorem for ordered spaces, Analysis, 9 (1989), 297–302,

[3] F. Moricz, Ordinary convergence follows from statistical summability (C, 1) in the case of slowly decreasing or oscillatingsequences, Colloq. Math., 99 (2004), 207–219,

[4] O. Talo, F. Basar, On the slowly decreasing sequences of fuzzy numbers, Abstr. Appl. Anal., (2013), Art. ID 891986,7 pp,

[5] G. H. Hardy, Divergent series, Oxford University Press, 1956,

[6] J. Karamata, Uber die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z., 32 (1930),319–320,

[7] K. Knopp, Theory and application of infinite series, Dover Publications, 1990,

[8] G. A. Mikhalin, Theorem of Tauberian type for (J, pn) summation methods, Ukrain. Mat. Zh., 29 (1977), 763–770,

[9] C. V. Stanojevic, V. B. Stanojevic, Tauberian retrieval theory, Publ. Inst. Math. (Beograd) (N.S.), 71 (2002), 105–111,

[10] A. Tauber, Ein satz aus der theorie der unendlichen reihen, Monatsh. f. Math. u. Phys., 7 (1897), 273–277,

Ibrahim Canak: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir-Turkey, [email protected]

Umit Totur: Adnan Menderes University, Faculty of Science, Department of Mathematics, Aydin-Turkey, utotur @ya-hoo.com


80 Positive Periodic Solutions for a Nonlinear First Order Func-tional Dynamic Equation by a New Periodicity Concept onTime ScalesErbil Cetin and F.Serap Topal

In this talk, we consider the existence, multiplicity and nonexistence of positive periodic solutions in shifts δ± for thenonlinear functional dynamic equation on a periodic time scale in shifts δ± with period P ∈ [t0,∞)T. By using the Kras-nosel’skii fixed point theorem and Leggett-Williams multiple fixed point theorem, we present different sufficient conditionsfor the existence of at least one, two or three positive solutions in shifts δ± of the problem on time scales. We extend andunify periodic differential, difference, h-difference and q-difference equations and more by a new periodicity concept on timescales.

References[1] E. Cetin, F.S. Topal, Periodic solutions in shifts δ± for a nonlinear dynamical equation on time scales, Abstract and Applied

Analaysis, Volume 2012, Article ID707319, 17 pages.2

[2] E.R. Kaufmann, Y. N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal.

Appl. 319 (2006) 315-325.

[3] M. Adıvar, A new periodicity concept for time scales, Math. Slovaca 63 (2013), No.4 817-828.

[4] M. Bohner and A. Peterson, Dynamic Equations on time scales, An Introduction with Applications, Birkhauser, Boston, 2001.

[5] M. Bohner, A. Peterson,(Eds) Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.

[6] S. Padhi, S. Srivastava, S. Pati, Three periodic solutions for a nonlinear first order functional differential equation, Applied

Mathematics and Computation 216 (2010) 2450-2456.

[7] S. Hilger, Ein MasskettenkalkA 14 l mit Anwendug auf Zentrumsmanningfaltigkeiten, Phd Thesis, Universitat Wurzburg,

1988.

[8] M.A. Krasnoselsel’skiı, Positive Solutions of Operator Equations Noordhoff, Groningen, 1964.

[9] X. L. Liu, W.T. Li, Periodic solution for dynamic equations on time scales, Nonlinear Analysis 67, no.5 (2007) 1457-1463.

[10] H. Wang, Positive periodic solutions of functional differential equations, J. Differential Equations, 202, (2004) 354-366.

[11] S. Padhi, S. Srivastava, Existence of three periodic solutions for a nonlinear first order functional differential equation, Journal

of the Franklin Institute 346 (2009) 818-829.

[12] Y. Li, L. Zhu, P. Liu, Positive Periodic Solutions of Nonlinear Functional Difference Equations Depending on a Parameter,

Computers and Mathematics with Applications 48 (2004) 1453-1459.

[13] A. Weng, J. Sun, Positive Periodic Solutions of first-order Functional Difference Equations with Parameter, Journal of Com-

putational and Applied Mathematics 229 (2009) 327-332.

[14] F. Qiuxiang, Y. Rong, On the Lasota-Wazewska model with piecewise constant arguments, Acta. Math. Sci. 26B(2)(2006)

371-378.

[15] D. Jiang, J. Wei, B. Jhang, Positive periodic solutions of functional differential equations and population models, Electron.

J. Differential Equations 71 (2002) 1-13.

[16] Y. Luo, W. Wang, J. Shen, Existence of positive periodic solutions for two kinds of neutral functional differential equations ,

Appl. Math. Lett. 21(6) (2008) 581-587.

[17] W.S.C Gurney, S.P. Blathe and R.M. Nishet, Nicholson’s blowflies revisited , Nature 287 (1980) 17-21.

[18] Y. Kuang, Delay Differential equations with Applications in Population Dynamics, Academic Press, New York, 1993.

[19] A. Wan, D. Jiang, A new existence theory for positive periodic solutions to functional differential equations , Comput. Math.

Appl. 47 (2004) 1257-1262.

[20] H.I. Freedman, J. Wu, Periodic solutions of single-species models with periodic delay, SIAM J. Math. Anal. 23 (1992) 689-701.

[21] K.P. Hadeler, J. Tomiuk, Periodic solutions of difference differential equations, Arch. Rational Mech. Anal. 65 (1977) 87-95.

[22] J.R. Graef, L. Kong, Existence of multiple periodic solutions for first order functional differential equations, Mathematical

and Computer Modelling 54 (2011) 2962-2968.

Erbil Cetin: Ege University, Faculty of Science, Department of Mathematics, Bornova Izmir-Turkiye, [email protected]

Fatma Serap Topal: Ege University, Faculty of Science, Department of Mathematics, Bornova Izmir-Turkiye, [email protected]


81 Potential Flow Field Around a TorusRajai Alassar

In this note, we present the potential flow field around a torus. We use the naturally fit toroidal coordinates system torecast the governing equation. We show that the governing equation has a series solution in terms of toroidal functions withcoefficients that satisfy a three-term recurrence relation.

King Fahd University of Petroleum & Minerals (KFUPM), Department of Mathematics and Statistics, KFUPM Box1620, Dhahran 31261, Saudi Arabia, [email protected]


82 On B−1-Convex Functions and Some InequalitiesGabil Adilov and Ilknur Yesilce

A subset U of Rn++ is B−1-convex if for all x, y ∈ U and all λ ∈ [1,∞) one has

λx ∧ y = (min λx1, y1 ,min λx2, y2 , ...,min λxn, yn) ∈ U.

For each kind of convex functions, some inequalities such as Hermite-Hadamard inequalities, Jensen inequalities, etc., areobtained by many authors ([1], [2], [3], etc.). In this work, similar inequalities are analyzed for B−1-convex functions.

References[1] G. Adilov, Increasing Co-radiant Functions and Hermite-Hadamard Type Inequalities, Mathematical Inequalities and

Applications, 14(1) (2011), 45-60,

[2] G. Adilov and S. Kemali, Abstract Convexity and Hermite-Hadamard Type Inequalities, Journal of Inequalities andApplications, 2009, Article ID 943534, doi:10.1155/953534, (2009), 13 pages,

[3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Mono-graphs, Victoria University, 2000, (ONLINE: http://ajmaa.org/RGMIA/monographs.php/).

Gabil Adilov: Akdeniz University, Faculty of Education, Department of Mathematics, Antalya-Turkey, [email protected] or [email protected]

Ilknur Yesilce: Mersin University, Faculty of Science and Letters, Department of Mathematics, Mersin-Turkey, [email protected]


83 On the Global Behaviour of a Higher Order Difference Equa-tionYasin Yazlik, D.Turgut Tollu and Necati Taskara

In this paper, we deal with the behavior well-defined solutions of the difference equation

xn = axn−1 +b+ xn−m − axn−m−1

c+ xn−m − axn−m−1, n ∈ N0,

where N0 = N ∪ 0 , the parameters a, b and c and the initial conditions x−m−1, x−m, . . . , x−1, x0 are real numbers.

References[1] R. P. Agarwal, Difference Equations and Inequalities, 1st edition, Marcel Dekker, New York, 1992, 2nd edition, 2000.

[2] V. L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, KluwerAcademic Publishers, Dordrecht, The Netherlands.

[3] R. P. Agarwal and E. M. Elsayed, Periodicity and stability of solutions of higher order rational difference equation,Adv. Stud. Contem. Math. 17(2) (2008), 181-201.

[4] L. Brand, A sequence defined by a difference equation. Am. Math. Mon. 62 (1955), 489-492.

[5] L. Berg, S. Stevic, On some systems of difference equations, Applied Mathematics and Computation 218 (2011),1713–1718.

[6] S. Stevic, On some solvable systems of difference equations, Applied Mathematics and Computation 218 (2012), 5010-5018.

[7] S. Stevic, M. A. Alghamdi, N. Shahzad and D. A. Maturi, On a class of solvable difference equations, Abstract AppliedAnalysis (2013), Article ID: 157943, 7 pages.

[8] I. Yalcinkaya, On the difference equation xn+1 = α+xn−mxkn

, Discrete Dynamics in Nature and Society (2008), Article

ID: 805460, 8 pages.

[9] S. E. Das and M. Bayram, Dynamics of a higher-order nonlinear rational difference equation, International Journal ofPhsical Sciences 6(12) (2011), 2950-2957.

[10] E.M.E. Zayed and M.A. El-Moneam, On the rational recursive sequence xn+1 = γxn−k +axn+bxn−kcxn−dxn−k

, Bulletin of the

Iranian Mathematical Society 36(1) (2010), 103-115.

[11] H. El-Metwally, E. M. Elsayed and E. M. Elabbasy, On the solutions of difference equations of order four, RockyMountain Journal of Mathematics 43(3), (2013), 877-894.

[12] S. Ozen, I. Ozturk and F. Bozkurt, On the recursive sequence yn+1 =α+yn−1

β+yn+

yn−1

yn, Applied Mathematics and

Computation 188 (2007), 180-188.

[13] C. Cinar, M. Toufik and I. Yalcinkaya, On the difference equation of higher order, Utilitas Mathematica 92 (2013),161-166.

[14] D. T. Tollu, Y. Yazlik and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonaccinumbers, Advances in Difference Equations 2013, 2013:174.

[15] I. Bajo, E. Liz, Global behaviour of a second-order nonlinear difference equation, J. Differ. Equations Appl. 17(10)(2011), 1471-1486,

[16] E.A. Grove, Y. Kostrov, G. Ladas, and S. W. Schultz, Riccati difference equations with real period-2 coeficients,Commun. Appl. Nonlinear Anal. 14 (2007), 33-56.

[17] G. Papaschinopoulos and B.K. Papadopoulos, On the Fuzzy Difference Equation xn+1 = A+ B/xn, Soft Computing6 (2002), 456-461.

[18] D. T. Tollu, Y. Yazlik and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics andComputation 233 (2014), 310-319.

Yasin Yazlık: Nevsehir Hacı Bektas Veli University, Faculty of Science and Art, Department of Mathematics, Nevsehir-Turkey, [email protected]

D. Turgut Tollu: Necmettin Erbakan University, Faculty of Science, Department of Mathematics-Computer Sciences,Konya-Turkey, [email protected]

Necati Taskara: Selcuk University, Science Faculty, Department of Mathematics, Konya-Turkey, [email protected]


84 Identifying an Unknown Time Dependent Coefficient for Qu-asilinear Parabolic EquationsFatma Kanca and Irem Baglan

This talk deals with the mathematical analysis of the inverse problem of identifying the unknown time-dependent coefficientin the quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. The existence,uniqueness and continuously dependence upon the data of the solution are proved by iteration method in addition to thenumerical solution of this problem is considered with an example.

References[1] F. Kanca, The inverse coefficient problem of the heat equation with periodic boundary and integral overdetermination

conditions, Journal of Inequalities and Applications, , 108 (2013), 1-9.

[2] F. Kanca, Inverse Coefficient Problem of the Parabolic Equation with Periodic Boundary and Integral OverdeterminationConditions, Abstract and Applied Analysis, 2013 (2013) 1-7.

[3] M. Ismailov, F. Kanca, An inverse coefficient problem for a parabolic equation in the case of nonlocal boundary andoverdetermination conditions, Mathematical Methods in the Applied Science, 34 (2011), 692-702.

[4] F. Kanca F.,Baglan I.,Continuous dependence on data for a solution of the quasilinear parabolic equation with a periodicboundary condition, Boundary Value Problems, 28 (2013).

[5] F. Kanca, I. Baglan, An inverse coefficient problem for a quasilinear parabolic equation with nonlocal boundary condi-tions”, Boundary Value Problems, 213 (2013).

[6] F. Kanca, I. Baglan ,An inverse problem for a quasilinear parabolic equation with nonlocal boundary and overdetermi-nation conditions, Journal of inequalities and applications, 76 (2014).

[7] I. Sakınc(Baglan) , Numerical Solution of a Quasilinear Parabolic Problem with Periodic Boundary Condition, Hacettepe,Journal of Mathematics and Statistics, 39 (2010), 183-189.

[8] A. M. Nakhushev, Equations of Mathematical Biology, Moscow, 1995 (in Russian).

[9] N. I. Ionkin, Solution of a boundary-value problem in heat conduction with a nonclassical boundary condition. Differ-ential Equations, 13 (1977), 204-211

Fatma Kanca: Department of Management Information Systems, Kadir Has University, 34083, Istanbul, Turkey, [email protected]

Irem Baglan: Department of Mathematics, Kocaeli University, Kocaeli 41380, Turkey,[email protected]


85 On Special Semigroup Classes and Congruences on SomeSemigroup ConstructionsSeda Oguz and Eylem Guzel Karpuz

The purpose of this study is to consider under which conditions Bruck-Reilly and generalized Bruck-Reilly*-extensionsmight belong to some special classes of semigroups such as regular, unit regular, completely regular, inverse, orthodox andE-unitary inverse. In addition to this we qualify the general types of congruences on generalized Bruck-Reilly*-extension.

References[1] J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press-Oxford, (1995),

[2] S. Oguz, E. G. Karpuz, Semigroup Properties on Bruck-Reilly and Generalized Bruck-Reilly ∗-Extensions of Monoids,in preparation,

[3] B. Piochi, Congruences on Bruck-Reilly extensions of monoids, Semigroup Forum 50 (1995), 179-191,

[4] Y. Shang, L. M. Wang, ∗-Bisimple Type A w2-Semigroups as Generalized Bruck-Reilly ∗-Extensions, Southeast AsianBulletin of Mathematics 32 (2008), 343-361.

Seda Oguz: Cumhuriyet University, Education Faculty, Department of Secondary School Science and MathematicsEducation, Sivas-Turkiye, [email protected]

Eylem Guzel Karpuz: Karamanoglu Mehmetbey University, Kamil Ozdag Science Faculty, Department of Mathematics,Karaman-Turkiye, [email protected]


86 The Rate of Pointwise Convergence of q−Szasz OperatorsTuncer Acar

In this talk, we mainly study on Voronovskaya type theorems for q−Szasz operators, defined in [Mahmudov, N. I., Onq−parametric Szasz-Mirakjan Operators, Mediterr. J. Math., 7 (2010), 297-311], and their q−derivatives. To do this,we consider the weighted spaces of approximation functions and related weighted modulus of continuity and we obtainquantitative Voronovskaya type theorem in terms of weighted modulus of continuity of q−derivatives of approximatingfunction. By this way, we either obtain the rate of pointwise convergence of q−Szasz operators and their derivatives or wepresent these results for continuous functions although classical ones are valid for differentiable functions.

References[1] Aral, A, Acar, T., Voronovskaya type result for q-derivative of q-Baskakov operators, J. Applied Func. Anal., 7 (4),

(2012), 321-331.

[2] Aral, A., A generalization of Szasz-Mirakyan operators based on q-integers, Math. Comput. Modelling, 47 (2008), no.9-10, 1052–1062.

[3] Aral, A., Gupta, V., The q-derivative and applications to q-Szasz Mirakyan operators, Calcolo 43 (2006), no. 3, 151–170.

[4] Aral, A., Gupta,V. and Agarwal, R. P., Applications of q-Calculus in Operator Theory, Springer, (2013).

[5] Finta, Z., Remark on Voronovskaja theorem for q-Bernstein operators, Stud. Univ. Bab·es-Bolyai Math. 56(2011), No.2, 335–339.

[6] Gasper, G., Rahman, M., Basic Hypergeometrik Series. Encyclopedia of Mathematics and Its Applications, vol. 35,Cambridge University Press, Cambridge, (1990).

[7] Kac, V., Cheung, P., Quantum Calculus, Springer, NewYork, (2002).

[8] Mahmudov, N. I., On q-parametric Szasz-Mirakjan Operators, Mediterr. J. Math., 7 (2010), 297-311.

[9] Mahmudov, N. I., q-Szasz-Mirakjan operators which preserve x2, J. Comput. Appl. Math. 235 (2011), no. 16, 4621–4628.

[10] Mahmudov, N. I., On q-parametric Szasz-Mirakjan operators, Mediterr. J. Math., 7 (2010), no. 3, 297–311.

[11] Philips, G. M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4 (1997), 511-518.

[12] Rajkovic, Predrag M., Stankovic, Miomir S., Marinkovic, Sla†ana D., Mean value theorems in q-calculus, Proceedingsof the 5th International Symposium on Mathematical Analysis and its Applications (Niska Banja, 2002), Mat. Vesnik54 (3-4) (2002), 171–178.

[13] Videnskii, V. S., On some classes of q-parametric positive linear operators, Operator Theory: Adv. and Appl., 158(2005), 213-222.

[14] Voronovskaya, E.V., Determination of the asymptotic form of approximation of functions by the polynomials of S.N.Bernstein, Dokl. Akad. Nauk SSSR, A, (1932), 79-85.

Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahsihan, 71450, Kirikkale-Turkey,[email protected]


87 Some Properties of Cohomology Groups for GraphsOzgur Ege and Ismet Karaca

In this work, we would like to construct cohomology theory for graphs. For this purpose, we deal with the singular homologyof graphs and take its dual structure. We then give the Universal coefficient theorem for singular cohomology in graphs.We show that the Kunneth theorem doesn’t yield for graphs. We also give explanatory examples on the topic. Lastly, wedeal with fixed point properties of graphs using singular cohomology groups.

References[1] E. Babson, H. Barcelo, M. Longueville and R. Laubenbacher, Homotopy theory of graphs, Journal of Algebraic Com-

binatorics, 24 (2006), 31-44.

[2] H. Barcelo, X. Kramer, R. Laubenbacher and C. Weaver, Foundations of a connectivity theory for simplicial complexes,Advances in Applied Mathematics, 26 (2001), 97-128.

[3] H. Barcelo and R. Laubenbacher, Perspectives on A-homotopy theory and its applications, Discrete Mathematics, 298(1-3) (2005), 39-61.

[4] A. Dochtermann, Hom complexes and homotopy theory in the category of graphs, European Journal of Combinatorics,30 (2009), 490-509.

[5] A. Dochtermann, Homotopy groups of Hom complexes of graphs, Journal of Combinatorial Theory, Series A 116(2009), 180-194.

[6] O. Ege and I. Karaca, ”The Lefschetz Fixed Point Theorem for Digital Images”, Fixed Point Theory and Applications,doi:10.1186/10.1186/1687-1812-2013-253, (2013).

[7] A. Granas and J. Dugundji, ”Fixed Point Theory”, Springer, 2003.

[8] V.V. Prasolov, Elements of Combinatorial and Differential Topology, American Mathematical Society, 2006.

[9] E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.

[10] M.E. Talbi and D. Benayat, The homotopy exact sequence of a pair of graphs, Acta Scientiarum Technology, (2013).

[11] M.E. Talbi and D. Benayat, Homology theory of graphs, Mediterranean Journal of Mathematics, (2013).

Ozgur Ege: Celal Bayar University, Faculty of Science and Letters, Department of Mathematics, Muradiye Campus,Manisa-Turkey, [email protected]

Ismet Karaca: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir-Turkey, [email protected]


88 Stability with Respect to Initial Time Difference for Gene-ralized Delay Differential EquationsRavi Agarwal and Snezhana Hristova

Stability with initial data difference of nonlinear delay differential equations is introduced and studied. This type of stabilitygeneralizes the known in the literature concept of stability. It gives us the opportunity to compare the behavior of twononzero solutions which initial values as well as initial intervals are different. Lyapunov functions as well as comparisonresults for scalar ordinary differential equations have been employed. Several examples will be given to illustrate bothconcepts and obtained results.

References[1] Agarwal R., Hristova S., Strict stability in terms of two measures for impulsive di erential equations with ”supremum”,

Appl. Analysis, 91, 7, 2012, 1379-1392.

[2] Bainov D., Hristova S. , Di erential Equations with ”Maxima”, Francis& Taylor, CRC Press, 2011.

[3] Jankowski T., Delay integro-di erential inequalities with initial time di erence and applications, J. Math. Anal. Appl.291 (2004) 605-624.

[4] Lakshmikantham V., Leela S., Devi J.V., Stability criteria for solutions of di erential equations relative to initial timedi erence, Int. J. Nonlinear Di . Eqns. 5 (1999) 109-114.

[5] Li A, Wei L, Ye J.,Exponential and global stability of nonlinear dynamical systems relative to initial time difference,Appl. Math. Comput. 217 (2011) 5923-5929 .

[6] Li A., Feng E., Li S., Stability and boundedness criteria for nonlinear di erential systems relative to initial timedifference and applications, Nonlinear Anal.: Real World Appl., 10 (2009) 1073–1080.

[7] Shaw M.D., Yakar C., Stability criteria and slowly growing motions with initial time di erence, Probl. Nonl. Anal. Eng.Sys. 1 (2000) 5066.

[8] Song X., Li A., Wang Zh., Study on the stability of nonlinear differential equations with initial time difference, NonlinearAnal.: Real World Appl. 11 (2010) 1304-1311.

[9] Song X., Li S., Li A., Practical stability of nonlinear differential equation with initial time difference, Appl. Math.Comput. 203 (2008) 157162

[10] Yakar C., Shaw M. , A Comparison result and Lyapunov stability criteria with initial time difference, Dynam. Cont.Discr. Impul. Sys.: Math. Anal. 12 (2005) 731–737.

[11] Yakar C., Shaw M.D., Initial time di erence stability in terms of two measures and variational comparison result,Dynam. Cont. Discr. Impul. Sys.: Math. Anal. 15 (3) (2008) 417-425.

[12] J. Henderson, S. Hristova, Eventual Practical Stability and cone valued Lyapunov functions for differential equationswith ”Maxima”, Commun. Appl. Anal., 14, 4, 2010, 515-524.

Ravi Agarwal: Texas A&M University-Kingsville, Department of Mathematics, Kingsville, TX 78363, USA, [email protected]

Snezhana Hristova: Plovdiv University, Faculty of Mathematics and Informatics, Department of Applied Mathematics,Bulgaria, [email protected]

Research was partially supported by Fund Scientific Research MU13FMI002, Plovdiv University.


89 On Ramanujan’s Summation Formula, his General ThetaFunction and a Generalization of the Borweins’ Cubic ThetaFunctionsChandrashekar Adiga

In Chapter 16 of his second notebook, Ramanujan develops two closely related topics, q-series and theta- functions. Inthe first part of the talk, we discuss about Ramunujan’s summation formula and his general theta function. The Borweinbrothers have introduced and studied three cubic theta functions. Many generalizations of these functions have been studiedas well. In the second part of the talk, we introduce a new generalization of these functions and establish general formulasthat are connecting our functions and Ramanujan’s general theta function. Many identities found in the literature followas a special case of our identities. We further derive general formulas for certain products of theta functions.

References[1] C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Chapter 16 of Ramanujan’s second notebook: Theta functions

and q-series, Mem. Amer. Math. Soc., 315 (1985), 1-91,

[2] B. C. Berdnt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991,

[3] S. Bhargava and S. N. Fathima, Laurent coefficients for cubic theta functions, South East Asian J. Math. Soc., 1 (2)(2003), 27-31,

[4] S. Bhargava and S. N. Fathima, Unification of modular transformations for cubic theta functions, New Zealand J. Math.,33 (2004), 121-127,

[5] J. M. Borwein and P. B. Borwein, Pi and AGM, Wiley, New York, 1987,

[6] J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi’s identity and the AGM, Trans. Amer. Math. Soc,323 (2) (1991), 691-701,

[7] S. Ramanujan, Notebooks (2 Volumes), Tata Institute of Fundamental Research, Bombay, 1957.

Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570 006, INDIA, c [email protected]


90 L∞ Error Estimate of Parabolic Variational Inequality Aris-ing of the Pricing of American OptionS.Madi, M.Hariour and M.C.Bouras

This contribution deals with the numerical analysis using the semi-implicit scheme with respect to t-variable combined withfinite element spacial approximation applied in parabolic variational inequalities arising from pricing of American option.Where the presented numerical result is efficient.

References[1] A. Bensoussan, J.L. Lions, Impulse control and quasi-variational inequalities, Gauthier Villars, Paris, (1984),

[2] P. Jaillet, D. Lamberton, and B. Lapeyre, Variational Inequalities and the Pricing of American Options, Acta Appli-candae Mathematicae 21: 263-289, 1990,

[3] M. Boulbrachene, M. Haiour, The finite element approximation of Hamilton Jacobi Bellman equations, Computers andMathematics with Applications, 41(2001), 993-1007,

[4] Y. Achdou , F. Hecht and D. PommierA Posteriori Error Estimates for Parabolic Variational Inequalities, J Sci Comput(2008), DOI 10.1007/s10915-008-9215-7,

[6] S. Boulaaras, M. Haiour, A new approach to asymptotic behavior for a finite element approximation in parabolicvariational inequalities, Hindawi Publishing Corporation, J. Mathematical Analysis, doi:10.5402/2011/703670.

LANOS Laboratory , Badji Mokthtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria, [email protected] work was supported by LANOS Laboratory of Annaba university-Algeria


91 The Smoothness of Convolutions of Zonal Measures on Com-pact Symmetric SpacesSanjiv Kumar Gupta and Kathryn Hare

We prove that for every compact symmetric space, Gc/K, of rank r, the convolution of any (2r + 1) continuous, K-bi-invariant measures is absolutely continuous with respect to the Haar measure on Gc. We also prove that the convolutionof (r + 1) continuous, K-invariant measures on the −1 eigenspace in the Cartan decomposition of the Lie algebra of Gc isabsolutely continuous with respect to Lebesgue measure. These results are nearly sharp.

References[1] Boudjemaa Anchouch, Sanjiv Kumar Gupta, Convolution of Orbital Mesaures in Symmetric Spaces, Bull. Aust. Math.

Soc. 83(2011), 470-485.

[2] Bump, D., Lie Groups, Graduate texts in mathematics 225, Springer, New York, 2004.

[3] Dunkl, C., Operators and harmonic analysis on the sphere, Trans. Amer. Math. Soc. 125(1966), 250-263.

[4] Gupta, S.K. and Hare, K.E., Singularity of orbits in SU(n), Israel J. Math. 130(2002), 93-107.

[5] Gupta, S.K. and Hare, K.E., Singularity of orbits in classical Lie algebras, Geom. Func. Anal. 13(2003), 815-844.

[6] Gupta, S.K. and Hare, K.E., Convolutions of generic orbital measures in compact symmetric spaces, Bull. Aust. Math.Soc. 79(2009), 513-522.

[7] Gupta, S.K. and Hare, K.E., L2-singular dichotomy for orbital measures of classical compact Lie groups, Adv. Math.222(2009), 1521-1573.

[8] Gupta, S.K. and Hare, K.E., Smoothness of convolution powers of orbital measures on the symmetric spaceSU(n)/SO(n), Monatsch. Math 159(2010), 27-43.

[9] Gupta, S.K., Hare, K.E. and Seyfaddini, S., L2-singular dichotomy for orbital measures of classical simple Lie algebras,Math. Zeit. 262(2009), 91-124.

[10] Humphreys, J., Introduction to Lie algebras and representation theory, Springer Verlag, New York, 1972.

[11] Helgason, S., Differential geometry, Lie groups and symmetric spaces, Academic Press, New York, 1978.

[12] Kane, R., Reflection groups and invariant theory, Canadian Math. Soc., Springer, N.Y., 2001.

[13] Knapp, A., Lie groups beyond an introduction, Birkhauser, Verlag AG (2002).

[14] Ragozin, D., Zonal measure algebras on isotropy irreducible homogeneous spaces, J. Func. Anal. 17(1974), 355-376.

[15] Ragozin, D., Central measures on compact simple Lie groups, J. Func. Anal. 10(1972), 212–229.

[16] F. Ricci and E. Stein, Harmonic analysis on nilpotent groups and singular integrals. II. Singular kernels supported onsubmanifolds, J. Func. Anal. 78(1988), 56–84.

[17] Wright, A., Sums of adjoint orbits and L2 -singular dichotomy for SU(m), Adv. Math. 227(2011), 253-266.

Sanjiv K. Gupta: Dept. of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36 Al Khodh 123, Sultanateof Oman, gupta.squ.edu.om

Kathryn E. Hare: Dept. of Pure Mathematics, University of Waterloo, Waterloo, Ont, Canada, N2L 3G1, [email protected]

The first author would like to thank the Dept. of Pure Mathematics for their hospitality while some of this researchwas done. This research was supported in part by NSERC and the Sultan Qaboos University.


92 A Tauberian Theorem for the Weighted Mean Method ofSummability of Sequences of Fuzzy NumbersZerrin Onder, Sefa Anıl Sezer and Ibrahim Canak

The notion of fuzzy set was realized by many researchers who are interested in Mathematics, Computer Science andEngineering and the idea was applied for studies in di?erent branches of science from different aspects. One of the areaswhich was applied it is the summability theory as well. In this talk, we focus on the weighted mean method of summabilityof sequences of fuzzy numbers and present a Tauberian theorem of slowly decreasing type. References

References[1] Y. Altin, M. Mursaleen and H. Altinok. Statistical summability (C,1) for sequences of fuzzy real numbers and a

Tauberian theorem. J. Intell. Fuzzy Systems, 21(6), 2010.

[2] S. Aytar, M. A. Mammadov and S. Pehlivan. Statistical limit inferior and limit superior for sequences of fuzzy numbers.Fuzzy Sets and Systems, 157(7):976-985, 2006.

[3] B. Bede. Mathematics of fuzzy sets and fuzzy logic. Springer, Berlin, 2013.

[4] I. Canak. On the Riesz mean of sequences of fuzzy real numbers. J. Intell. Fuzzy Systems, DOI:10.3233/IFS- 130938.

[5] I. Canak. Tauberian theorems for Cesaro summability of sequences of fuzzy numbers. J. Intell. Fuzzy Systems,DOI:10.3233/IFS-131053.

[6] D. Dubois and H. Prade. Operations on fuzzy numbers. Internat. J. Systems Sci., 9(6):613-626, 1978.

[7] D. Dubois and H. Prade. Fuzzy sets and systems. Mathematics in Science and Engineering. Academic Press, NewYork-London, 1980.

[8] R. Goetschel and W. Voxman. Elementary fuzzy calculus. Fuzzy Sets and Systems, 18(1):31-43, 1986.

[9] M. Matloka. Sequences of fuzzy numbers. Busefal, 28:28-37, 1986.

[10] F. Moricz and B.E. Rhoades. Necessary and su?cient Tauberian conditions for certain weighted mean methods ofsummability. II. Acta Math. Hung., 102(4):279-285, 2004.

[11] S. Nanda. On sequences of fuzzy numbers. Fuzzy Sets and Systems, 33(1):123-126, 1989.

[12] P. V. Subrahmanyam. Cesaro summability for fuzzy real numbers. J. Anal., 7:159-168, 1999.

[13] O. Talo and F. Basar. On the slowly decreasing sequences of fuzzy numbers. Abstr. Appl. Anal., pp. Art. ID 891986,7, 2013.

[14] O. Talo and C. C akan. On the Cesaro convergence of sequences of fuzzy numbers. Appl. Math. Lett., 25(4):676- 681,2012.

[15] B. C. Tripathy and A. Baruah. Norlund and Riesz mean of sequences of fuzzy real numbers. Appl. Math. Lett.,23(5):651-655, 2010.

[16] L. A. Zadeh. Fuzzy sets. Information and Control, 8:338-353, 1965.

Zerrin Onder: Ege University, Department of Mathematics, 35100, Izmir, Turkey, [email protected] Anıl Sezer: Ege University, Department of Mathematics, 35100, Izmir, Turkey, [email protected], se-

[email protected]

Ibrahim Canak: Ege University, Department of Mathematics, 35100, Izmir, Turkey, [email protected],ibrahim.canak @ege.edu.tr


93 Asymptotic Constancy for a System of Impulsive Delay Dif-ferential EquationsFatma Karakoc and Huseyin Bereketoglu

In this talk, we investigate a class of impulsive delay differential equations system. First, convergence of solution is proved.Then a formula is obtained for the limit of the solution.

References[1] F.V. Atkinson, J.R. Haddock, Criteria for asymptotic constancy of solutions of functional-differential equations. JMAA

91 (2) 410-423 (1983).

[2] H. Bereketoglu and M. Pituk, Asymptotic constancy for nonhomogeneous linear differential equations with unboundeddelays, Discrete and Continuous Dynamical Systems, Supp. Vol., (2003) 100-107.

[3] F. Karakoc and H. Bereketoglu, Some results for linear impulsive delay differential equations. Dynamics of Continuous,Discrete and Impulsive Systems Series A: 16, 313-326, (2009).

Fatma Karakoc: Ankara University, Faculty of Science, Department of Mathematics, Ankara-Turkey, [email protected]

Huseyin Bereketoglu: Ankara University, Faculty of Science, Department of Mathematics, Ankara-Turkey, [email protected]


94 An Extension w with rankw = 3 of a Valuation v on a FieldK with rankv = 2 to K(x)Figen Oke

Let v = v1ov2 be a valuation on a field K with rankv = 2. In this study an extension w = w1ow2ow3 of v such thatrankw = 3 and w2 is trivial over the residue field kv1 is defined and its properties are investigated.

References[1] V. Alexandru, N. Popescu, A. Zaharescu, A theorem of characterization of residual transcendental extension of a

valuation, J. Math. Kyoto Univ. 28 (1988), 579-592.

[2] V. Alexandru, N. Popescu, A. Zaharescu, Minimal pair of definition of a residual transcendental extension of a valuation,J. Math. Kyoto Univ. , 30 (1990), no. 2, 207-225

[3] V. Alexandru, N. Popescu, A. Zaharescu, All valuations on K(X), J. Math. Kyoto Univ. , 3 (1990), no. 2, 281-296.

[4] N. Bourbaki, Algebre Commutative, Ch. V: Entiers, Ch. VI: Valuations, Hermann, Paris (1964).

[5] O. Endler, Valuation Theory, Springer, Berlin -Heidelberg-New York (1972).

[6] N. Popescu, C. Vraciu, On the extension of valuations on a field K to K(x)-I, Ren. Sem. Mat. Univ. Padova, 87 (1992),151-168

[7] N. Popescu, C. Vraciu On the extension of valuations on a field K to K(x)-II, Ren. Sem. Mat. Univ. Padova, 96 (1996),1-14

[8] O.F.G. Schilling, The Theory of Valuations, A.M.S. Surveys, no. 4, Providence, Rhode Island (1950).

Trakya University Department of Mathematics, Edirne, Turkey, [email protected]


95 Inclusions Between Weighted Orlicz SpaceAlen Osanclıol

Let (X,Σ, µ) be a measure space and Φ be a Young function. The weighted Orlicz space with weight ω is denoted by LΦω (X)

and it is a natural generalization of the weighted Lebesgue space in which characterization of inclusion is well known. In this

talk, we investigate the inclusion between weighted Orlicz spaces LΦ1w1 (X) and LΦ2

w2 (X) with respect to Young functions Φ1,Φ2 and weights w1, w2. We also define the weighted Orlicz norm and show that the inclusion map is continuous. Moreover,in case of X = Rn with Lebesgue measure on Rn, we give a necessary and sufficient conditions on weights for the equalityof two weighted Orlicz spaces when Φ1 = Φ2.

References[1] H.G. Feichtinger, Gewichtsfunktione nauf lokal kompakten Gruppen, Sitzungsberichte der Osterr. Akad d Wissenchaften,

Mathem-naturw, Klasse, AbteilungII, (1979), 188, Bd, 8. bis 10,

[2] M. M. Rao and Z.D. Ren, Theory of Orlicz Spaces, CRC Press, 1 edition, 1991,

[3] A. Villani, A Note on the Inclusion Lp(µ) ⊂ Lq(µ), The American Mathematical Monthly, Vol.92 (1985), No.7, 485-487,

Sabancı University, Faculty of Engineering and Natural Sciences, Tuzla, Istanbul-Turkey, [email protected] work was supported by the Scientific Research Projects Coordination Unit of Istanbul University, Project number

14671.


96 On the Some Graph Parameters for Special GraphsNihat Akgunes, Ahmet Sinan Cevik and Ismail Naci Cangul

In this talk, we discuss some graph parameters for important special graphs, for instance, ladder graph. Actually, then-ladder graph can be defined as P2Pn, where Pn is a path graph. We aim to implement some algorithms for computingthe some important graph parameters for that graphs. We will investigate some good result for some parameters of thatgraphs.

References[1] H. Hosoya, and F. Harary, On the Matching Properties of Three Fence Graphs. J. Math. Chem., 12 (1993), 211-218.

[2] M. Noy, and A. Ribo, Recursively Constructible Families of Graphs. Adv. Appl. Math. 32 (2004), 350-363.

[3] C. P. Mooney, Generalized Irreducible Divisor Graphs, Communications in Algebra, 42-10 (2014), 4366-4375, DOI:10.1080/00927872.2013.811246

[4] R. Chang, and Z. Yan, On The Harmonic Index and The Minimum Degree of A Graph, Romanian Journal of InformationScience And Technology 15-4 (2012), 335-343.

[5] L. Zhong, The harmonic index for graphs, Applied Mathematics Letters 25-3 (2012), 561-566

[6] H. Deng, S. Balachandran, S. K. Ayyaswamy and Y. B. Venkatakrishnan, On the harmonic index and the chromaticnumber of a graph. Discrete Applied Mathematics, 161-16 (2013)., 2740-2744.

[7] N. Akgunes, K.C. Das, A.S. Cevik, Topological indices on a graph of monogenic semigroups, in: Ivan Gutman (Ed.),Topics in Chemical Graph Theory, Mathematical Chemistry Monographs, University of Kragujevac and Faculty ofScience Kragujevac, Kragujevac,( 2014), ISBN 978-86-6009-027-2. No.16a, IV+262 pp

Nihat Akgunes: Necmettin Erbakan University, Faculty of Science, Department of Mathematics-Computer Sciences,Konya- Turkiye, [email protected]

Ahmet Sinan Cevik: Selcuk University, Faculty of Science, Department of Mathematics, Konya-Turkiye, [email protected]

Ismail Naci Cangul: Uludag University, Faculty of Science, Department of Mathematics, Bursa-Turkiye, [email protected]

This work was partially supported by the Necmettin Erbakan University, Selcuk University, Uludag University.


97 A Note on the Dirichlet-Neumann First Eigenvalue of a Fam-ily of Polygonal Domains in R2

A.R.Aithal and Acushla Sarswat

Let ℘1 and ℘0 be closed, regular, convex, concentric polygons having n sides in R2 such that the circumradius of ℘0 isstrictly less than the inradius of ℘1. We fix ℘1 and vary ℘0 by rotating it about its center. Let Ω be the interior of ℘1 \℘0.In this paper we examine the behaviour of the first Dirichlet-Neumann eigenvalue λ1(Ω) through a variation of the domain.

References[1] A. E. Soufi and R. Kiwan, Extremal First Dirichlet Eigenvalue of Doubly Connected Plane Domains and Dihedral

Symmetry, SIAM J. Math. Anal., 39(4)(2007), pp. 1112-1119,

[2] A. R. Aithal and R. Raut, On the Extrema of Dirichlet’s First Eigenvalue of a Family of Punctured Regular Polygonsin Two Dimensional Space Forms, Proc. Indian Acad. Sci. Math. Sci., 122(2012), pp. 257-281,

[3] G. B. Folland, Introduction to Partial Differential Equations, Second Edition, Prentice-Hall of India, New Delhi, 2001,

[4] P. Grisvard, Singularities in Boundary Value Problems,Recherches en Mathematiques Appliques 22, Masson, Paris;Springer-Verlag, Berlin, 1992,

[5] J. Sokolowski and J. P. Zolesio, Introduction to Shape Optimization-Shape Sensitivity Analysis, Springer-Verlag, 1992.

A.R. Aithal: Department of Mathematics, University of Mumbai, Vidyanagari, Mumbai 400 098, India, [email protected]

Acushla Sarswat: Department of Mathematics, University of Mumbai, Vidyanagari, Mumbai 400 098, India, [email protected]


98 An Approach to the Numerical Verification of Solutions forVariational InequalitiesC.S.Ryoo

In this talk, we describe a numerical method to verify the existence of solutions for a unilateral boundary value prob-lems for second order equation governed by the variational inequalities. It is based on Nakao’s method by using finiteelement approximation and its explicit error estimates for the problem. Using the Riesz present theory in Hilbert space,we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixedpoint theory, we construct a high efficiency numerical verification method that through numerical computation generates abounded, closed, convex set in which includes the approximate solution. Finally, a numerical example is illustrated.

References[1] N. W. Bazley, D. W. Fox, Comparision operators for lower bounds to eigenvalues, J. reine angew. Math., 223(1966)

142-149.

[2] J. Cea, Optimisation, theorie et algorithmes, Paris: Dunod, 1971.

[3] X. Chen, A verification method for solutions of nonsmooth equations, Computing, 58(1997) 281-294.

[4] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North–Holland, Amsterdam, 1978.

[5] R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer, New York, 1984.

[6] I. Hlavacek, J. Haslinger, J. Necas, J. Lovısek, Solution of Variational Inequalities in Mechanics, Springer Ser. Appl.Math. Sci., 66, 1988.

[7] T. Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan, 4(1949) 334-339.

[8] N. J. Lehmann, Optimale Eigenwerteinschließungen, Numer. Math., 5(1963) 246-272.

[9] U. Mosco, Approximation of the solutions of some variational inequalities, Roma: Press of Roma University, 1971.

[10] M. T. Nakao, A numerical verification method for the existence of weak solutions for nonlinear boundary value problems.Journal of Math. Analysis and Appl.164(1992) 489-507.

[11] Y. Watanabe, N. Yamamoto, M. T. Nakao, Verified computations of solutions for nondifferential elliptic equationsrelated to MHD equilibria. Nonlinear Analysis, Theory, Mathods & Applications, 28(1997) 577-587.

[12] F. Natterer, Optimale L2-Konvergenz finiter Elemente bei Variationsungleichungen. Bonn. Math. Schr.89(1976) 1-12

[13] M. Plum, Explict H2-Estimates and Pointwise Bounds for Solutions of Second-Order Elliptic Bounday Value Problems.Journal of Mathematical Analysis and Appl.165(1992)36-61

[14] M. Plum, Enclosures for weak solutions of nonlinear elliptic boundary value problems, WSSIAA, World ScientificPublishing Company, 3(1994) 505-521.

[15] M. Plum, Existence and Enclosure Results for Continua of Solutions of Parameter -Dependent Nonlinear BoundaryValue Problems, Journal of Computational and Applied Mathematics, 60(1995) 187-200.

[16] S. M. Rump, Solving algebraic problems with high accuracy, A new approach to scientific computation ( Edited byU. W. KULISH and W. L. MIRANKER ), Academic Press, New York, 1983, pp. 51-120.

[17] C. S. Ryoo, Numerical verification of solutions for a simplified Signorini problem, Comput. Math. Appl., 40(2000)1003-1013.

[18] C.S. Ryoo, An approach to the numerical verification of solutions for obstacle problems, Computers and Mathematicswith Applications, 53 (2007), 842-850.

[19] C.S. Ryoo, Numerical verification of solutions for Signorini problems using Newton-like mathod, International Journalfor Numerical Methods in Engineering, 73 (2008), 1181-1196.

[20] C.S. Ryoo and R.P. Agarwal, Numerical inclusion methods of solutions for variational inequalities, InternationalJournal for Numerical Methods in Engineering, 54 (2002), 1535-1556.

[21] C.S. Ryoo and R.P. Agarwal, Numerical verification of solutions for generalized obstacle problems, Neural, Parallel& Scientific Compuataions, 11 (2003), 297-314.

[22] C.S. Ryoo and M.T. Nakao, Numerical verification of solutions for variational inequalities, Numerische Mathematik,81 (1998), 305-320.

[23] F. Scarpini, M. A. Vivaldi, Error estimates for the approximation of some unilateral problems. R.A.I.R.O. NumericalAnalysis, 11(1977) 197-208.

[24] G. Strang, G. Fix, An analysis of the finite element method. Englewood Cliffs, New Jersey, Prentice-Hall, 1973.

Department of Mathematics, Hannam University, Daejeon 306-791, Korea, [email protected]


99 Local Rings and Projective Coordinate SpacesFatma Ozen Erdogan and Suleyman Ciftci

In this paper; some properties of modules constructed over the real plural algebra A are investigated and also a moduleover the linear algebra of matrix K = Mmm(R) is constructed. Then, projective coordinate spaces over a local ring R areaddressed. Finally, the concept of a projective space over a vector space is generalized to a space over a module by the helpof equivalence classes.

References[1] B. R. McDonald, Geometric algebra over local rings, New York: Marcel Dekker, 1976,

[2] F. Machala, Fundamentalsatze der projektiven Geometrie mit Homomorphismus, Rozpravy CSAV, Rada Mat. Prirod.Ved, 90, 5, 1980,

[3] H. Lenz, Vorlesungen uber projektive Geometrie I. Leipzig, 1965,

[4] J.W.P. Hirschfeld, Projective Geometries over Finite Fields. Oxford Science Publications, New York, 1998,

[5] K. Nomizu, Fundamentals of Linear Algebra, New York, McGraw-Hill, 1966,

[6] M. Jukl, Linear forms on free modules over certain local ring, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math.,32 (1993), 49-62,

[7] M. Jukl, Grassmann formula for certain type of modules, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 34(1995), 69-74,

[8] M. Jukl, V. Snasel, Projective equivalence of quadrics in Klingenberg Projective Spaces over a special local ring,International Journal of Geometry, 2 (2009), 34-38,

[9] R. Lingenberg, Grundlagen der Geometrie I. Bibliographisches Institut Mannheim (Wien) Zurich, 1969,

[10] T. W. Hungerford, Algebra, New York, Holt, Rinehart and Winston, 1974.

Fatma Ozen Erdogan: Uludag University, Faculty of Science, Department of Mathematics, Gorukle, Bursa-Turkiye,[email protected]

Suleyman Ciftci: Uludag University, Faculty of Science, Department of Mathematics, Gorukle, Bursa-Turkiye, [email protected]

This work is supported by The Research Fund of University of Uludag Project number KUAP(F)-2012/56.


100 An Improved Numerical Solution of the Singular BoundaryIntegral Equation of the Compressible Fluid Flow AroundObstacles Using Modified Shape FunctionsLuminita Grecu

In this work an improved numerical solution of the singular boundary integral equation of the 2D copressible fluid flowaround obstacles is obtained by a boundary element method based on modified shape functions and cubic boundary elements.The singular boundary integral equation with sources distribution is considered in this paper, and, for its discretization,cubic boundary elements are used. The integrals of singular kernels are evaluated using modified shape functions which arededuced by using series expansions for the basis functions choose for the local approximation models. A computer codeis made using Mathcad programming language, and based on it some particular cases are solved. In order to validate theproposed method, comparisons between numerical solutions and exact ones are performed for the considered test problems.A comparison between the numerical solution obtained by the method proposed and the one obtained by a method thatalso uses cubic boundary elements but doesn’t use modified shape functions for evaluating the singularities is also made.

References[1] H.M.Antia, Numerical Methods for Scientists and Engineers, Birkhausen, 2002

[2] M. Bonne, Bounndary integral equation methods for solids and fluids, John Wiley and Sons, 1995.

[3] C.A. Brebbia, J.C.F.Telles, L.C.Wobel, Boundary Element Theory and Application in Engineering, Springer-Verlag,Berlin,1984.

[4] L. Dragos, Mathematical Methods in Aerodinamics, Editura Academiei Romane, Bucuresti, 2000.

[5] L. Dragos, Fluid Mechanics I, Editura Academiei Romane, Bucuresti, 1999.

[6] L. Grecu, A solution of the boundary integral equation of the theory of infinite span airfoil in subsonic flow with linearboundary elements, Annals of the University of Bucharest, Year LII, Nr. 2(2003), 181-188.

[7] L. Grecu, A solution with cubic boundary elements for the compressible fluid flow around obstacles, Boundary ValueProblems 2013 2013:78

[8] IK. Lifanov, Singular integral equations and discrete vortices, VSP, Utrecht, The Netherlands, 1996.A. Carabineanu,A boundary element approach to the 2D potential flow problem around airfoils with cusped trailing edge, ComputerMethods in Applied. Mechanics and Engineering. 129(1996), 213-219

[9] I. Vladimirescu, L. Grecu, Weakening the Singularities when Applying the BEM for 2D Compressible Fluid Flow, LectureNotes in Engineering and Computer Science: Proc. of The International MultiConference of Engineers and ComputerScientists 2010, Hong Kong, 2224-2229

University of Craiova, Department of Applied Mathematics, Craiova, Romania, [email protected]


101 New Aspects of Calculating Volumes in EnDaniela Bittnerova and Daniela Bımova

The talk presents an alternative approach to the calculation of the volumes of solids in n-dimensional Euclidean spaceand shows some applications of that theory, including the proof of the formula for it. The mentioned method uses basictopological properties, among others. To solve volumes of solids, we must find suitable parametric descriptions of surfaceareas of given solids. These surface areas must be smooth or piecewise smooth areas in Euclidean space of the correspondingdimensions. The advantage of the theory could be in the using of integrals of the dimension less then n. This contributionalso refers to correspondence between the curvilinear and surface integral theory for calculations of areas of closed figures,respectively volumes of solids, and the results of the alternative theory. However, it is kept generally in n-dimensional spacefor the alternative theory.

References[1] D. Bittnerova, Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas, AIP Conf.

Proc. 1570, 3 (2013),

[2] D. Bittnerova , P. Cervenkova , The Corollary of Gauss-Ostrogradsky Theorem, Proceedings of XXX. InternationalColloquium. Brno, 2012,

[3] S. Huggett, D. Jordan, A Topological Aperitiv, Springer-Verlang, 2001, ISBN 1-85233-377-4,

[4] S. Dineen, Multivariate Calculus and Geometry, Springer-Verlag, 2001, ISBN 1-85233-472-X.

Daniela Bittnerova: Technical University of Liberec, Faculty of Science, Humanities and Education, Department ofMathematics and Didactics of Mathematics, Liberec - Czech Republic, [email protected]

Daniela Bımova: Technical University of Liberec, Faculty of Science, Humanities and Education, Department of Math-ematics and Didactics of Mathematics, Liberec - Czech Republic, [email protected]

The paper was supported by the project SGS - FP - TUL 2014 ”Nonlinear Parameterization - applications using graphicsoftware”. Special thanks to students H. Vacatova, P. Vurmova, and D. Vacata for their help with solving examples.


102 Applications of an Alternative Methods for Volumes ofSolids of RevolutionDaniela Bımova and Daniela Bittnerova

In this talk, we connect the contribution New Aspects of Calculating Volumes in En in this congress where an alternativetheory for calculations of volumes of solids in the n-dimensional Euclidean space is presented. Now we discuss the applicationof that theory to volumes of solids of revolution with circular and elliptical perpendicular sections (sphere, toroid, axoid,horn toroid, melanoid). The proofs of the formulas of the alternative theory mentioned above are given for that type ofsolids. Using the mentioned theory, the formulas of volumes computed solids of revolution are simpler than the general onesare.

References[1] D. Bittnerova, Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas, AIP Conf.

Proc. 1570, 3 (2013),

[2] D. Bittnerova, Parameterization and Volume of a Torus, ICPM 07 Conf. Proc., Liberec (2007),

[3] S. Huggett, D. Jordan, A Topological Aperitiv, Springer-Verlang, 2001, ISBN 1-85233-377-4,

[4] S. Dineen, Multivariate Calculus and Geometry, Springer-Verlag, 2001, ISBN 1-85233-472-X.

Daniela Bımova: Technical University of Liberec, Faculty of Science, Humanities and Education, Department of Math-ematics and Didactics of Mathematics, Liberec - Czech Republic, [email protected]

Daniela Bittnerova: Technical University of Liberec, Faculty of Science, Humanities and Education, Department ofMathematics and Didactics of Mathematics, Liberec - Czech Republic, [email protected]

The paper was supported by the project SGS - FP - TUL 2014 ”Nonlinear Parameterization - applications using graphicsoftware”. Special thanks to students H. Vacatova, P. Vurmova, and D. Vacata for their help with solving examples anddrawing figures.


103 On Certain Sums of Fibonomial CoefficientsEmrah Kılıc and Aynur Yalcıner

In this talk, we present some classes of sums formulas including Fibonomial coefficients with finite product of generalizedFibonacci and Lucas numbers as coefficients. We translate everything into q-notation and then use generating function andRothe’s identity to prove them.

References[1] G. E. Andrews, R. Askey, R. Roy, Special functions, Cambridge University Press, 2000,

[2] H. W. Gould, The bracket function and Fontene-Ward generalized binomial coefficients with application to Fibonomialcoefficients, The Fibonacci Quarterly, 7 (1969), 23-40,

[3] V. E. Hoggatt Jr., Fibonacci numbers and generalized binomial coefficients, The Fibonacci Quarterly, 5 (1967), 383-400,

[4] A. F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke Math. J., 32(1965), 437-446,

[5] E. Kılıc, The generalized Fibonomial matrix, European J. Combinatorics, 31 (2010), 193-209,

[6] E. Kılıc, H. Prodinger, I. Akkus, H. Ohtsuka, Formulas for Fibonomial Sums with generalized Fibonacci and Lucascoefficients, The Fibonacci Quarterly, 49:4 (2011), 320-329,

[7] E. Kılıc, H. Prodinger, Closed form evaluation of sums containing squares of Fibonomial coefficients, accepted inMathematica Slovaca.

[8] E. Kılıc, H. Ohtsuka, I. Akkus, Some generalized Fibonomial sums related with the Gaussian q-binomial sums, Bull.Math. Soc. Sci. Math. Roumanie, 55:103, No. 1, (2012), 51-61,

[9] D. Marques, P. Trojovsky, On Some New Sums of Fibonomial Coefficients, The Fibonacci Quarterly, 50:2 (2012),155-162,

[10] P. Trojovsky, On some identities for the Fibonomial coefficients via generating function, Discrete Appl. Math., 155:15,(2007), 2017-2024.

Emrah Kılıc: TOBB University of Economics and Technology, Mathematics Department, 06560 Ankara, Turkey, [email protected]

Aynur Yalcıner: Selcuk University, Faculty of Science, Department of Mathematics , Campus 42075, Konya, Turkey,[email protected].


104 Null Generalized Helices of a Null Frenet Curve in L4

Esen Iyigun

In this paper; we study the null generalized helices in view of curvature functions and harmonic curvatures in 4-dimensionalLorentzian space for two time-like and two null vectors by using the Frenet frame in [2] for a null curve.

References[1] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983,

[2] K. L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer AcademicPublishers, Dordrecht, Boston, London, 1996,

[3] F. A. Yalınız, H. H. Hacısalihoglu, Null Generalized Helices in Lm+2, Bull. Malays. Math. Sci. Soc. (II), 30(1) (2007),74-85,

[4] N. Ekmekci, H. H. Hacısalihoglu and K. Ilarslan, Harmonic Curvatures in Lorentzian Space, Bull. Malays. Math. Sci.Soc. (Second Series), 23 (2000), 173-179,

[5] R. Aslaner, A. I. Boran, On The Geometry of Null Curves in The Minkowski 4-space, Turk. J. Math., 33 (2009),265-272,

[6] A. Altın, Harmonic Curvatures of Null Curves and The Null Helix in Rm+21 , International Mathematical Forum, 2(23)

(2007), 1111-1118,

Uludag University, Faculty of Science, Department of Mathematics, Gorukle, Bursa-Turkiye, [email protected]


105 Geometrical Methods and Numerical Computations forPrey-Predator Lotka-Volterra SystemsAdela Ionescu, Romulus Militaru and Florian Munteanu

The purpose of this paper is to study symmetries and conservation laws for the mathematical model of the multi-speciesinteractions, given by Volterra-Lotka equations. We will recall the Hamilton-Poisson realisations of 2D and 3D Volterra-Lotka systems and we use the geometric formalism to obtain new conservation laws starting from symmetries. Our study isa interplay between dynamical systems geometrical theory and computational calculus of dynamical systems, knowing thatthe theory provides a framework for interpreting numerical observations and foundations for algorithms.

References[1] P. Gao, Hamiltonian structure and first integrals for the Lotkaa“Volterra systems, Physics Letters A, 273 (2000), 85-96.

[2] B. Grammatjcos, J. Moulin-Ollagnier, A. Ramani, J. M. Strelcyn and S. Wojciechowski, Integrals of quadratic ordinarydifferential equations in R3: the Lotka-Volterra system, Physica A 163 (1990) 683-722.

[3] R. Militaru, F. Munteanu, Geometric Methods for the Study of Biodynamical Systems. Symmetries and ConservationLaws, Proc. 9th Int. Conf. Cellular and Molecular Biology, Biophysics and Bioengineering(BIOa) Chania, Crete, Greece,August 27-29, 2013, pp. 54-61.

[4] R. Militaru, F. Munteanu, Symmetries and Conservation Laws for Biodynamical Systems, Int. J. of Math. Models andMethods in Applied Sciences, Issue 12, Vol. 7 (2013), pp. 965-972.

[5] Y. Nutku, Hamiltonian structure of the Lotka-Volterra equations, Physics Letters A, 145 (1) (1990), 27-28.

[6] P.J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 107, Springer-Verlag,New York, 1986.

[7] R. Tudoran, A. Gırban, On a Hamiltonian version of a three-dimensional Lotka-Volterra system, Nonlinear Analysis:Real Word Applications, 13 (2012), 2304-2312.

Adela Ionescu: Department of Applied Mathematics, University of Craiova, Al. I. Cuza 13, Craiova 200585, Romania,[email protected]

Romulus Militaru: Department of Applied Mathematics, University of Craiova, Al. I. Cuza 13, Craiova 200585,Romania, [email protected]

Florian Munteanu: Department of Applied Mathematics, University of Craiova, Al. I. Cuza 13, Craiova 200585,Romania, [email protected]

This work was partially supported by the grant number 19C/2014, awarded in the internal grant competition of theUniversity of Craiova.


106 Fractional Calculus Model of Dengue EpidemicMoustafa El-Shahed

This paper deals with the fractional order dengue epidemic model. The stability of disease free and positive fixed points isstudied. Adams–Bashforth–Moulton algorithm have been used to solve and simulate the system of differential equations.

Department of Mathematics, Faculty of Art and Sciences, P.O. Box 3771, Unizah-Qassim, Qassim University, SaudiArabia, [email protected]


107 Zagreb Co Indices and Augmented Zagreb Index and itsPolynomials of Phenylene and Hexagonal SqueezeP.S.Ranjini, V.Lokesha and Usha.A

The topological indices are the graph invariants obtained from the molecular graphs corresponding to the structural featuresof organic molecules. A topological index of a chemical compound characterizes the compound and obeys a particular rule.In this paper, we find the Augmented Zagreb index, Zagreb Co−indices, Zagreb Co−indices polynomials and AugmentedZagreb polynomials for Phenylene and Hexagonal Squeeze.

Ranjini P.S: Department of Mathematics, Don Bosco Institute Of Technology,Bangalore-74, India, ranjini p [email protected]

V. Lokesha: Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Bellary, India, [email protected]

Usha.A: Department of Mathematics, Alliance College of Engineering and Design, Alliance University, Anekal-Chandapura Road, Bangalore, India, [email protected]


108 A Note on Class Numbers of Real Quadratic Fields withCertain Fundamental DiscriminantsAyten Pekin

ONO, proved a theorem in by applying Sturm’s Theorem on the congruence of modular form to Cohen’s half integral weightmodular forms. Later, Dongho Byeon proved a theorem and corollory by refining Ono’ methods. In this paper, we will givea theorem for certain real quadratic fields by considering above mentioned studies. To do this, we shall obtain an upperbound different from current bounds for L(1, χD) and use Dirichlet’s class number formula.

Department of Mathematics, Faculty of Science, Istanbul University, 34134 Istanbul-Turkey, [email protected]


109 On Three Dimensional Dynamical Systems on Time ScalesElvan Akın

In this talk, motivated by Thandapani and Ponnamal [6], we investigate oscillation and asymptotic properties of solutionsof three dimensional systems of first order dynamic equations on a time scale, nonempty closed subset of real numbers. Thetheory of dynamic equations on time scales has been created in order to unify continuous and discrete analysis, see booksby Bohner and Peterson [4] and [5]. We also refer the readers to manuscripts by Akin, Dosla, Lawrence [2], [3] and Akguland Akin [1].

References[1] Akgul, A. and Akin, E., Almost oscillatory three dimensional dynamical systems of first order delay dynamic equations,

Nonlinear Dynamics and Systems Theory. To appear, 2014.

[2] Akin-Bohner, E., Dosla , Z., and Lawrence, B. Oscillatory properties for three dimensional dynamic systems. NonlinearAnal., 69 (2) (2008) 483-494.

[3] Akin-Bohner, E., Dosla, Z., and Lawrence, B. Almost oscillatory three-dimensional dynamical system. Adv. DifferenceEqu., 46 (2012) 14 pages.

[4] Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications. Birkhauser,Boston, 2001.

[5] Bohner, M. and Peterson, A., Advances in Dynamic Equations on Time Scales. Birkhauser, Boston, 2003.

[6] Thandapani, E. and Ponnammal, B. Oscillatory properties of solutions of three-dimensional difference systems. Math.Comput. Modelling, 45 (5-6) (2005) 641-650.

Missouri University Science Technology 400 W 12th Street Rolla, MO, 65409-0020, USA


110 On the Difference Equation System xn+1 = 1+ynyn, yn+1 = 1+yn

xnNecati Taskara, Durhasan Turgut Tollu and Yasin Yazlik

In this paper, we mainly consider the system of difference equations xn+1 = 1+ynyn

, yn+1 = 1+ynxn

, n ∈ N0 where initial

conditions x0 and y0 are real numbers such that the denominators are always nonzero. We give exact information aboutthe behavior of solutions of the system.

References[1] R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York (1992),

[2] M. R. S. Kulenovic and O. Merino, Discrete Dynamical Systems and Difference Equations with Mathematica, Chap-man&Hall/CRC Press, (2002),

[3] L. Brand, A sequence defined by a difference equation. Am. Math. Mon. 62 (1955), 489-492,

[4] D. T. Tollu, Y. Yazlik, N. Taskara, On the Solutions of two special types of Riccati Difference Equation via FibonacciNumbers, Advances in Difference Equations, (2013), 2013:174,

[5] E.A. Grove, Y. Kostrov, G. Ladas, and S. W. Schultz , Riccati difference equations with real period-2 coeficients,Commun. Appl. Nonlinear Anal., 14 (2007), 33-56,

[6] G. Papaschinopouls and B.K. Papadopoulos, On the Fuzzy Difference Equation , Soft Computing, 6 (2002), 456-461,

[7] I. Yalcinkaya, C. Cinar, M. Atalay, On the Solutions of Systems of Difference Equations, Advances in DifferenceEquations, Vol. (2008), Article ID 143943,

[8] D. T. Tollu, Y. Yazlik, N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics andComputation, 233 (2014), 310-319,

[9] L. Berg, S. Stevice, On some systems of difference equations, Appl. Math. Comput. 218 (2011) 1713–1718,

[10] S. Stevice. On some solvable systems of difference equations, Appl. Math. Comput. 218 (2012) 5010–5018,

[11] N. Taskara, K. Uslu and D.T. Tollu, The periodicity and solutions of the rational difference equation with periodiccoefficients, Computers & Mathematics with Applications, 62 (2011), 1807-1813.

Necati Taskara: Selcuk University, Faculty of Science, Department of Mathematics, Selcuklu, Konya-Turkiye, [email protected]

D.T. Tollu: Necmettin Erbakan University, Faculty of Science, Department of Mathematics-Computer Sciences, Meram,Konya-Turkiye, [email protected]

Y. Yazlik: Nevsehir Haci Bektas Veli University, Faculty of Science and Art, Department of Mathematics, 50300,Nevsehir-Turkiye, [email protected]


111 The Binomial Transforms of Tribonacci and Tribonacci-Lucas SequencesNazmiye Yilmaz and Necati Taskara

In this study, we apply the binomial transforms to Tribonacci and Tribonacci-Lucas sequences. Also, the Binet formulas,summations, generating functions of these transforms are found using recurrence relations. Finally, we illustrate the relationbetween these transforms by deriving new formulas.

References[1] K.W. Chen, Identities from the binomial transform, Journal of Number Theory 124, (2007), 142-150,

[2] S. Falcon, A. Plaza, Binomial transforms of k-Fibonacci sequence, International Journal of Nonlinear Sciences andNumerical Simulation 10(11-12), (2009), 1527-1538,

[3] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY (2001),

[4] H. Prodinger, Some information about the binomial transform, The Fibonacci Quarterly 32 (5), (1994), 412-415,

[5] N. Yilmaz, N. Taskara, Binomial transforms of the Padovan and Perrin matrix sequences, Abstract and Applied Analysis,Article Number: 497418 Published: 2013,

[6] M. Elia, Derived sequences, the Tribonacci recurrence and cubic forms, The Fibonacci Quarterly 39(2), (2001), 107-109,

[7] Y. Yazlik, N. Yilmaz, N. Taskara, The Binomial Transforms of the generalized (s,t)-matrix sequence, 4th InternationalConference of Matrix Analysis and Applications (ICMAA2013), Konya 2013,

[8] M. Feinberg, Fibonacci-Tribonacci, The Fibonacci Quarterly 1(3), (1963), 70-74,

[9] A.N. Philippou, A. A. Muwafi, Waiting for the Kth consecutive success and the Fibonacci sequence of order K, TheFibonacci Quarterly 20(1), (1982), 28-32,

[10] W.R. Spickerman, Binet’s formula for the Tribonacci sequence, The Fibonacci Quarterly 20(2), (1982), 118-120,

[11] M. Catalani, Identities for Tribonacci-related sequences, Cornell University Library, (2002), avaliable athttp://http://arxiv.org/abs/math/0209179v1.

[12] L. Marek-Crnjac, On the mass spectrum of the elementary particles of the standard model using El Naschie’s goldenfield theory, Chaos, Solutions & Fractals, 15(4) (2003), 611-618.

[13] L. Marek-Crnjac, The mass spectrum of high energy elementary particles via El Naschie’s golden mean nested oscilla-tors, the Dunkerly-Southwell eigenvalue theorems and KAM, Chaos, Solutions & Fractals, 18(1) (2003), 125-133.

[14] P. Bhadouria, D. Jhala, B. Singh, Binomial Transforms of the k-Lucas Sequences and its Properties, Journal ofmathematics and computer science, 8, (2014), 81-92.

Nazmiye Yilmaz: Selcuk University, Faculty of Science, Department of Mathematics, Selcuklu, Konya-Turkiye, [email protected]

Necati Taskara: Selcuk University, Faculty of Science, Department of Mathematics, Selcuklu, Konya-Turkiye, [email protected]


112 On the Random Functional Central Limit Theorems withAlmost Sure Convergence for SubsequencesZdzislaw Rychlik

In this talk, we present functional random-sum central limit theorems with almost sure convergence for independent non-identically distributed random variables. We consider the case where the summation random indices and partial sums areindependent. In the past decade several authors have investigated the almost sure functional central limit theorems andrelated ’logarithmic’ limit theorems for partial sums of independent random variables. We extend this theory to almost sureversions of the functional random-sum central limit theorems for subsequences.

References[1] I. Berkes, E. Csaki, A universal result in almost sure central limit theory, Stochastic Process. Appl., 94 (2001), 105-134,

[2] I. Berkes, E. Csaki, S. Csorgo, Almost sure limit theorems for the St. Petersburg game, Statist. Probab. Lett., 45 (1999),23-3,

[3] M. Csorgo, L. Horvath, Invariance principles for logarithmic averages, Math. Proc. CambridgePhilos. Soc., 112 (1992),195-205,

[4] I. Fazekas, Z. Rychlik, Almost sure functional limit theorems, Ann. Univ. Mariae Curie-Sk lodowska, 56(1) (2002),1-18,

[5] M. T. Lacey, W. Philipp, A note on the almost sure central limit theorem, Statist. Probab. Lett., 9 (1990), 201-214,

[6] B. Rodzik, Z. Rychlik, An almost sure central limit theorem for independent random variables, Ann. Inst. H. Poincare,30 (1994), 1-11,

[7] Z. Rychlik, K. S. Szuster, On the strong versions of the central limit theorem, Statist. Probab. Lett., 61 (2003), 348-357,

[8] Z. Rychlik, K. S. Szuster, On the random functional central limit theorems with almost sure convergence for subse-quences, Demonstratio Mathematica, XLV(2) (2012), 283-296,

[9] P. Schatte, On the central limit theorems with almost sure convergence, Probab. Math. Statist., 11 (1991), 315-343,

Maria Curie-Sk lodowska University, Faculty of Mathematics, Physics and Computer Science, Lublin-Poland and StateSchool of Higher Education, Che lm-Poland, [email protected]


113 Some Fixed Point Theorems for a Pair of Mappings inComplex Valued b-Metric SpacesAiman Mukheimer

In this paper, we generalize and study the results of M. Kutbi et al, by improving the conditions of the contraction whichis the product and the quotient of metrics, and we establish the existence and uniqueness of common coupled fixed pointsfor a pair of mappings on complex valued b-metric spaces.

Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia


114 Some Characterizations of Slant Curves on Unit Dual SphereS2

Seda Oral and Mustafa Kazaz

In this paper, we consider the dual Darboux frame e, t, g of a ruled surface in Euclidean 3-space E3. By the aid of theE.Study Mapping, a ruled surface can be consider as a dual spherical curve. Then, we define some new types of curves onunit dual sphere S2 , called slant dual curves that each vector of Darboux frame makes a constant dual angle with somefixed directions in dual 3-space D3. Furthermore, we give some characterizations for a curve to be a slant dual curve whichis important for differential geometry, surface geometry and especially surface design theory.

References[1] Ali, A., T., Position vectors of slant helices in Euclidean Space E3. Journal of Egyptian Mathematical Society, V.

20(1), 2012, 1-6.

[2] Barros, M., General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125, no.5, (1997) 1503-1509.

[3] Blaschke, W., ”Differential Geometrie and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover”, NewYork, (1945).

[4] Karger, A., Novak, J., Space Kinematics and Lie Groups. STNL Publishers of Technical Lit., Prague, Czechoslovakia(1978).

[5] Kula, L., Ekmeki, N., Yayl, Y., larslan, K., Characterizations of Slant Helices in Euclidean 3-Space, Turk J Math., 33(2009) 1-13.

[6] Struik, D., J., Lectures on Classical Differential Geometry, 2nd ed. Addison Wesley, Dover, (1988).

[7] O’Neill, B., ”Semi-Riemannian Geometry with Applications to Relativity”, Academic Press, London, (1983).

[8] Onder, M., Slant ruled surfaces in Euclidean 3-space E3.

[9] Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation. 169, (2005),600-607.

Seda Oral: Celal Bayar University, Muradiye, Manisa, Turkey, [email protected] Kazaz: Celal Bayar University, Faculty of Science and Arts, Department of Mathematics, Muradiye Campus,

Manisa, Turkey, [email protected]


115 On Solving Some Partial Differential EquationsUmit Sarp and Sebahattin Ikikardes

In this talk, the numerical solutions of some partial differential equations have been analyzed by using DifferentialTransform Method and the obtained results are compared with other numerical methods. The study show us that theresults obtained by using Differential Transform Method are compatible with the existing solutions. Also DifferentialTransform Method can easily be adapted to many computer programs.

References[1] Arikoglu, A. and Ozkol, I., (2006). Solution of differential-difference equations by using differential transform method.

Applied Mathematics and Computation, Issue 181(1), pp. 153-162.

[2] Ayaz, F., (2003). On the two-dimensional differential transform method. Applied Mathematics and Computation, Issue143, pp. 361-374.

[3] Ayaz, F., (2004). Applications of differential transform method to differential-algebraic equations. Applied Mathematicsand Computation, Issue 152, no. 3, p. 649–657.

[4] Ayaz, F., (2004). Solutions of the system of differential equations by differential transform Method. Applied Mathe-matics and Computation, Cilt 147, p. 547–567.

[5] Chen, C. K. and Ho, S. H., (1996). Application of differential transformation to eigenvalue problems. Applied Mathe-matics and Computation, pp. 173-188.

[6] Chen, C. K. and Ho, S. H., (1999). Solving partial differential equations by two-dimensional differential transformmethod. Applied Mathematics and Computation, Issue 106, p. 171–179.

[7] Hassan, A. H. and I., H., (2002). Different applications for the differential transformation in the differential equations.Applied Mathematics and Computation, 2-3(129), p. 183–201.

[8] Hassan, A. H. and I., H., (2002). On solving some eigenvalue problems by using a differential Transformation. AppliedMathematics and Computation, Issue 127, p. 1–22.

[9] Jang, M. J., Chen, C. L. and Liu, Y. C., (2001). Two-dimensional differential transform for partial differential equations.Applied Mathematics and Computation, Issue 121, pp. 261-270.

[10] Keskin, Y. and Oturanc, G., (2009). Reduced differential transform method for partial differential equations. Interna-tional Journal of Nonlinear Sciences and Numerical Simulation, 6(10), pp. 741-749.

[11] Kurnaz, A., Oturanc, G. and Kiris, . E. M., (2005). n-Dimensional differential transformation method for solving PDE.International Journal of Computer Mathematics, 3(82), pp. 369-380.

[12] Zhou, J. K., (1986). Differential Transformation and Its Applications for Electrical Circuits. Huazhong University Press.

Umit Sarp: Balikesir University, Faculty of Arts and Science Department of Mathematics, Cagis Campus Balikesir-Turkey, [email protected], [email protected]

Sebahattin Ikikardes: Balikesir University Faculty of Arts and Science Department of Mathematics, Cagis CampusBalikesir-Turkey [email protected], [email protected]

This work was supported by the Scientific Research Projects Unit of Balikesir University, Project number 2014/155.


116 Some Spectrum Properties in C∗- AlgebrasNilay Sager and Hakan Avcı

We show that if ϕ is a ∗ - homomorphism between unital commutative C∗- algebras A and B with A−1 = ϕ−1(B−1

), then

property of mapping of spectrum is satisfied and adjoint mapping ϕ∗ : ∆(B) → ∆(A) is surjective, that is, maximal idealspace of B maps to maximal ideal space of A.

References[1] E. Kaniuth, A Course in Commutative Banach Algebras, Springer - Verlag, New York, 2009,

[2] J. Dixmier, C∗- Algebras, Elsevier North - Holland Publishing Company, Inc., 1977,

[3] M. Takesaki, Theory of Operator Algebras I, Springer - Verlag, New York, 1979,

[4] W. Rudin, Functional Analysis, Second Edition, McGraw - Hill, Inc., 1991,

[5] R. Larsen, Banach Algebras : An Introduction, Marcel Dekker, 1973,

[6] M. Bresar, S. Spenko, Determining Elements in Banach Algebras Through Spectral Properties, Journal of MathematicalAnalysis and Applications, 393 (2012), 144 - 150,

[7] B. Russo, Linear Mappings of Operator Algebras, Proceedings of the American Mathematical Society, 17 (1966), 1019-1022,

[8] T. W. Palmer, Jordan ∗ - Homomorphisms Between Reduced Banach ∗ - Algebras, Pacific Journal of Mathematics, 58(1975), 169-178,

[9] I. Kovacz, Invertibility - Preserving Maps of C∗- Algebras With Real Rank Zero, Abstract and Applied Analysis, 6(2005), 685-689.

Nilay Sager: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit, Samsun-Turkey, [email protected]

Hakan Avcı: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit, Samsun-Turkey, [email protected]


117 On Function Spaces with Fractional Fourier Transform inthe Weighted Lebesgue SpacesErdem Toksoy and Ayse Sandıkcı

Let w and ω be weight functions on Rd. In this work, we define Aw,ωα,p

(Rd)

to be the vector space of f ∈ L1w

(Rd)

such that the fractional Fourier transform belongs to Lpω(Rd)

for 1 ≤ p < ∞. We endow this space the sum norm

‖f‖Aw,ωα,p= ‖f‖1,w + ‖Fαf‖p,ω and show that Aw,ωα,p

(Rd)

becomes a Banach space and invariant under time frequence

shifts. Further we show that the mapping y → Tyf is continuous from Rd into Aw,ωα,p

(Rd)

and the mapping z → Mzf is

continuous from d into Aw,ωα,p

(Rd)

and Aw,ωα,p

(Rd)

is a Banach Module over L1w

(Rd)

with Θ convolution operation. At theend of this work, we discuss inclusion properties of these spaces. Some key references are given below.

References[1] A. Bultheel, H. Martinez, A Shattered Survey of the Fractional Fourier Transform, Department of Computer Science,

K.U.Leuveven, Report TW337, 2002,

[2] H. G. Feichtinger, A. T. Gurkanlı, On a Family of Weighted Convolution Algebras, Internat. J. Math. Sci, 13 (1990),517-526,

[3] R. H. Fischer, A. T. Gurkanlı and T. S. Liu, On a Family of Weighted Spaces, Math. Slovaca, 46 (1) (1996), 71-82,

[4] V. Namias, The Fractional Order of Fourier Transform and its Application in Quantum Mechanics, Journal of theInstitute of Mathematics and its Applications, 25 (1980), 241-265,

[5] H. M. Ozaktas, M. A. Kutay and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and SignalProcessing, John Wiley & Sons Ltd, England, 2001,

[6] A. Sahin, H. M. Ozaktas and D. Mendlovic, Optical Implementations of Two-Dimensional Fractional Fourier Transformsand Linear Canonical Transforms with Arbitrary Parameters, Applied Optics, 37 (11) (1998), 2130-2141,

[7] A. K. Singh, R. Saxena, On Convolution and Product Theorems for FRFT, Wireless Pers Commun, 65 (2012), 189-201,

Erdem Toksoy: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit,Samsun-Turkey, [email protected]

Ayse Sandıkcı: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit,Samsun-Turkey, [email protected]


118 Some Convergence Results for Modified SP-Iteration Schemein Hyperbolic SpacesAynur Sahin and Metin Basarır

In this study, we prove some strong and ∆-convergence theorems for a modified SP-iteration scheme for total asymptoticallynonexpansive mappings in hyperbolic spaces by employing recent technical results of Khan et. al. [An implicit algorithmfor two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl. (2012) 2012:54]. The resultspresented here extend and improve some well known results in the current literature.

References[1] Kohlenbach, U: Some logical metatheorems with applications in functional analysis. Trans. Amer. Math. Soc. 357(1),

89-128 (2004)

[2] Goebel, K, Reich, S: Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings. Marcel Dekker, New York(1984)

[3] Bridson, M, Haefliger, A: Metric Spaces of Non-Positive Curvature. Springer, Berlin (1999)

[4] Chang, SS, Wang, L, Joesph Lee, HW, Chan, CK, Yang, L: Demiclosed principle and ∆-convergence theorems for totalasymptotically nonexpansive mappings in CAT(0) spaces. Appl. Math. Comput. 219, 2611-2617 (2012)

[5] Fukhar-ud-din, H, Kalsoom, A, Khan, MAA: Existence and higher arity iteration for total asymptotically nonexpansivemappings in uniformly convex hyperbolic spaces. arXiv:1312.2418v2 [math.FA] (2013)

[6] Phuengrattana, W, Suantai, S: On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuousfunctions on an arbitrary interval. J. Comput. Appl. Math. 235, 3006-3014 (2011)

[7] Khan, AR, Fukhar-ud-din, H, Khan, MAA: An implicit algorithm for two finite families of nonexpansive maps inhyperbolic spaces. Fixed Point Theory Appl. (2012) 2012:54, doi:10.1186/1687-1812-2012-54

[8] Zhao, LC, Chang, SS, Wang, XR: Convergence theorems for total asymptotically nonexpansive mappings in hyperbolicspaces. J. Appl. Math. vol. 2013, Article ID 689765, 5 pages (2013)

[9] Sahin, A, Basarır, M: On the strong and 4-convergence of SP-iteration on a CAT(0) space. J. Inequal. Appl. (2013)2013:311, doi: 10.1186/1029-242X-2013-311

[10] Dhompongsa S, Panyanak, B: On 4-convergence theorems in CAT(0) spaces. Comput. Math. Appl. 56(10), 2572–2579(2008)

[11] Leustean, L: Nonexpansive iterations in uniformly convex W-hyperbolic spaces. In: Leizarowitz, A, Mordukhovich,BS, Shafrir, I, Zaslavski, A (eds.), Nonlinear Analysis and Optimization I: Nonlinear Analysis, Contemp. Math., Am.Math. Soc. AMS 513, 193–209 (2010)

Aynur Sahin: Sakarya University, Faculty of Sciences and Arts, Department of Mathematics, Sakarya-Turkey, [email protected]

Metin Basarır: Sakarya University, Faculty of Sciences and Arts, Department of Mathematics, Sakarya-Turkey,[email protected]

This work was supported by the Commission of Scientific Research Projects of Sakarya University, Project number2013-02-00-003.


119 Characterization of W p−type of Spaces Involving Frac-tional Fourier TransformS.K.Upadhyay and Anuj Kumar

The characterizations of W p−type of spaces and mapping relations between W and W ptype of spaces are discussed byusing fractional Fourier transform. The uniqueness of Cauchy problems is also investigated by using the same transform.

S.K. Upadhyay: DST-CIMS and Department of Mathematical Sciences Indian Institute of Technology (BHU), Varanasi-221 005, India, [email protected]

Anuj Kumar: ST-CIMS, Faculty of Science, Banaras Hindu University, Varanasi-221 005, India, [email protected]


120 Rates of Convergence for an Estimator of a Density Func-tion Based on Hermite PolynomialsElif Ercelik and Mustafa Nadar

Let X1, X2, ... be a sequence of i.i.d random variables with unknown density function f . We investigate the mean integratedsquare error convergency rate of an estimator based on Hermite polynomials for an unknown density function f whichincorporate certain delta sequences.

Walter [8] and Greblicki and Pawlak [1] studied the mean integrated square error (MISE) convergency rate of theestimator based on Hermite series method. Later on, Letellier [2] studied MISE convergency rate of the estimator based ondelta sequences by using Jakobi polynomials. In this work we obtained MISE convergency rate of the estimator based on

delta sequences by using Hermite polynomials as O

(N−rr+1

)which is faster than that of Walter and Letellier and slower

than of Greblicki and Pawlak.

References[1] Greblicki W., Pawlak M., ”Hermite Series Estimates of a Probability Density and Its Derivatives”, Journal of Multi-

variate Analysis 15, 174-182, 1984.

[2] Letellier J. A., ”Rates of convergence for an estimator of a density function based on Jakobi polynomials”, Communi-cation in Statistics- Theory and Methods, 26:1, 197-220, 1997.

[3] Nadar M., “Local convergence rate of mean squared error in density estimation”, Communication in Statistics- Theoryand Methods, Vol 40, pp. 176-185, 2011.

[4] Susarla V. , Walter G., “Estimation of a multivariate density function using delta sequences”, Annals of Statistics,Vol.9, pp. 347-355, 1981.

[5] Szego G., ”Orthogonal Polynomials”, American Mathematical Society, 1939.

[6] Timan A. F., “Theory of Approximation of Functions of a Real Variable”, Oxford, England: Pergammon Press, 1963.

[7] Walter G., Blum.J., “Probability density estimation using delta sequences”, Annals of Statistics, Vol.7, pp. 328-340,1979.

[8] Walter G., ”Properties of Hermite Series Estimation of Probability Density”, Annals of Statistics, Vol.5.No. 6, 1258-1264, 1977.

[9] Zygmund A., “Trigonometric Series”, New York: Chelsea Publishing Company, 1952.

Elif Ercelik: Gebze Institute of Technology, Department of Mathematics, Kocaeli, Turkey and Istanbul TechnicalUniversity, Department of Mathematical Engineering, Istanbul, Turkey, [email protected] or [email protected]

Mustafa Nadar: Istanbul Technical University, Department of Mathematical Engineering, Istanbul, Turkey, [email protected]


121 Estimation of Reliability in Multicomponent Stress-StrengthModel Based on Marshall–Olkin Weibull DistributionMustafa Nadar and Fatih Kızılaslan

We consider a system which have k identical strength components and each component is a random vector (X11, X12), (X21,X22), . . . , (Xk1, Xk2) following Marshall–Olkin Bivariate Weibull distribution with Parameters ( σ, θ1, θ2, θ3). Let Zi =min(Xi1, Xi2), i = 1, . . . , k.The system is regarded as operating only if at least s out of k (1 ≤ s ≤ k) strength variablesexceeds a random stress Y which has Weibull distribution with parameters ( σ, α). Then, when σ is known, the reliabilityRs,k in the described multicomponent stress-strength model is obtained as

Rs,k =k∑i=s

k−i∑j=0

(ki

)(k − ij

)(−1)jα

[θ(i+ j) + α]

where θ = θ1 + θ2 + θ3.Finally, a Monte Carlo Simulation study is performed to compare the reliability using both maximum likelihood and

Bayesian estimation.

References[1] Bhattacharyya, G.K., Johonson, R.A. 1974. Estimation of reliability in multicomponent stress-strength model, Journal

of the American Statistical Association, 69, 966-970.

[2] G. Srinivasa Rao, Muhammad Aslam, Debasis Kundu 2014. Burr-XII Distribution parametric estimation and estimationof reliability of multicomponent stress-strength, Comm. Statist.-Theory and Meth.,

[3] Davarzani, N., Haghighi, F., Parsian, A. 2009. Estimation of P (X ≤ Y ) for a Bivariate Weibull Distribution, Journalof Applied Probability & Statistics, 4(2): 227-238.

[4] Marshall, A.W., Olkin, I., 1967. A multivariate exponential distribution. Journal of the American Statistical Association62, 30–44.

Mustafa Nadar: Istanbul Technical University, Department of Mathematical Engineering, Istanbul, Turkey, [email protected]

Fatih Kızılaslan: Gebze Institute of Technology, Department of Mathematics, Kocaeli, Turkey, [email protected]


122 Some New Results on The Π−Regularity of Some MonoidsAhmet Emin and Fırat Ates

In this talk we give some new results on the regularity and Π -Regularity of Schetzenberger and Crossed products ofmonoids.

References[1] ] A. Emin, F.Ates, S.Ikikardes, I.N.Cangul, A New Monoid Construction Under Crossed Product, Journal of Inequalities

and Applivations,2013:244

[2] Y.Zhang, S.Li, D.Wang, semidirect products and wreath products of strongly - inverse monoids, GeorgianMath.Journal,3(3) (1996),293-300

[3] F.Ates, Some New Monoid And Group Constructions Under Semidirect Products. , Ars.Comb.91,203-218,2009

[4] E.G.Karpuz, F.Ates, S.Cevik, Regular and -Inverse Monoids Under Schetzenberger Products, Algebras Groups AndGeometries 27,455-471,2010

[5] J.M.Howie, N.Ruskuc, Construction and Presentations For Monoids, Communications In Algebra, 22(15),6209-6224,1994

[6] E.G.Karpuz, A.S.Cevik, A New Example Of Strongly -inverse monoids,Hacettepe Journal Of Mathematics and Statis-tics , 40(3),461-468,2011

Ahmet Emin: Balikesir University, Faculty of Art and Science, Department of Mathematics, Cagıs Campus, Balıkesir-Turkiye, [email protected]

Fırat Ates: Balikesir University, Faculty of Art and Science, Department of Mathematics, Cagıs Campus, Balıkesir-Turkiye, [email protected]


123 On Traveling Wave Solutions of Fractional Differential Equa-tionsSerife Muge Ege and Emine Mısırlı

In this work, the space-time fractional Hirota-Satsuma-Coupled KdV equation and the space-time fractional Fokas equationare handled by using the modified Kudryashov method. Consequentially, many analytical exact solutions are obtainedincluding rational solutions and symmetrical Fibonacci function solutions. This method is powerful, effectual and can beused as an alternative to constitute new solutions of various types of fractional differential equations applied in scientificfields.

References[1] N. A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonl. Sci.

Numer. Simul., 17 (2012), 2248-2253,

[2] S. M. Ege, E. Misirli, The modified Kudryashov method for solving some evolution equations, AIP Conf. Proc., 1470(2012), 244-246,

[3] S. M. Ege, E. Misirli, The modified Kudryashov method for solving some fractional-order nonlinear equations, Advancesin Difference Equations, 135 (2014), 1-13,

[4] S. M. Ege, E. Misirli, Solutions of the space-time fractional foam-drainage equation and rhe fractional Klein-Gordonequation by use of modified Kudryashov method, International Journal of Research in Advent Technology, 2321(9637)(2014), 384-388,

[5] M. M. Kabir, Modified Kudryashov method for generalized forms of the nonlinear heat conduction equation, Int. J.Phys. Sci., 6 (2011), 6061-6064,

[6] M. M. Kabir, A. Khajeh, E. A. Aghdam, A. Y. Koma, Modified Kudryashov method for finding exact solitary wavesolutions of higher-order nonlinear equations, Math. Meth. Appl. Sci., 34 (2011), 244-246,

[7] A. Stakhov, B. Rozin, On a new class of hyperbolic functions, Chaos, Solitons Fract., 23 (2005), 379-389,

[8] G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions furtherresults, Compt. Math. Appl., 51, (2006) 1367-1376,

[9] G. Jumarie, Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution,J. Appl. Math. Compt., 24, (2007) 31-48.

Serife Muge Ege: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir-Turkiye, [email protected]

Emine Mısırlı: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir-Turkiye, [email protected]

This research is supported by Ege University, Scientific Research Project (BAP), Project Number: 2012FEN037.


124 On the Oscillation of Second Order Nonlinear Neutral Dy-namic Equations on Time ScalesElvan Akın, Can Murat Dikmen and Said Grace

In this talk, we investigate some new oscillation criteria and give sufficient conditions to ensure that all solutions ofsecond order nonlinear neutral dynamic equations with distributed deviating arguments are oscillatory on a time-scaleT, via comparison with second order nonlinear dynamic equations whose oscillatory character are known and extensivelystudied in the literature.

References[1] E. Akın-Bohner, Z. Dosla, B. Lawrence, Oscillatory properties for three-dimensional dynamic systems, Nonlinear

Analysis, 69 : 483-494, 2008.

[2] M. Bohner and A. Peterson Dynamic equations on Time Scales: An Introduction with Applications, Birkhauser, Boston,2001.

[3] T. Candan, Oscillation of second order nonlinear neutral dynamic equations on time scales with distributed deviatingarguments, Comput. Math. Appl., 62 : 4118-4125, 2011.

[4] S.R. Grace, R.P. Agarwal, B. Kaymakcalan and W. Sae-Jie, On the oscillation of certain second order nonlineardynamic equations, Math. Comput. Modelling, 50 : 273-286, 2009.

[5] S.R. Grace, R.P. Agarwal, M. Bohner and D. O’Regan, Oscillation of second order strongly superlinear and stronglysublinear dynamic equations, Commun. Nonlin. Sces. Numer. Simulat., 14 : 3463-3471, 2009..

Elvan Akın: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO65409, USA, [email protected]

Can Murat Dikmen: Bulent Ecevit Universitesi, Fen-Edebiyat Fakultesi, Matematik Bolumu, 67100 Zonguldak, Turkey,[email protected]

Said Grace: Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Gizza 12221,Egypt, [email protected]


125 A Collocation Approach to Parabolic Partial DifferentialEquationsKubra Erdem Bicer and Salih Yalcınbas

In this study, a collocation approach is presented to solve parabolic partial differential equations. For this, an approximatemethod based on Bernoulli polynomials is developed. The method we have used consists of reducing the problem to amatrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on thematrix forms of Bernoulli polynomials and their derivatives by means of collocations. Also error analysis and a numericalexample are presented to demonstrate the validity and applicability of the technique.

References[1] K. Erdem, S.Yalcınbas, Bernoulli Polynomial Approach to High-Order Linear Differential-Difference Equations, AIP

Conf. Proc. 1479 (2012) 360-364.

[2] K. Erdem, S.Yalcınbas, Numerical approach of linear delay difference equations with variable coefficients in terms ofBernoulli polynomials, AIP Conf. Proc. 1493 (2012) 338-344.

[3] K. Erdem, S. Yalcınbas.,M. Sezer, “A Bernoulli Polynomial Approach with Residual Correction for Solving MixedLinear Fredholm Integro-Differential-Difference Equations ”, Journal of Difference Equations and Applications, vol:19,s:1619-1631.

[4] Paul M.N. Feehan, Camelia A. Pop, “A Schauder approach to degenerate-parabolic partial differential equations withunbounded coefficients”, Journal of Differential Equations, 254 (2013) 4401–4445.

[5] Yuan-Ming Wang, “Error and extrapolation of a compact LOD method for parabolic differential equations”, Journal ofComputational and Applied Mathematics 235 (2011) 1367–1382.

[6] Suayip Yuzbasi, Niyazi Sahin, “Numerical solutions of singularly perturbed one-dimensional parabolic convection–diffusion problems by the Bessel collocation method”, Applied Mathematics and Computation 220 (2013) 305–315.

Kubra Erdem Bicer: Celal Bayar University, Faculty of Science, Department of Mathematics, Manisa, Turkey, [email protected]

Salih Yalcinbas: Celal Bayar University, Faculty of Science, Department of Mathematics, Manisa, Turkey, [email protected]


126 From Simplicial Homotopy to Crossed Module HomotopyI.Ilker Akca and Kadir Emir

As is known from [1, 3, 5], simplicial algebras with Moore complex of length 1 (2) lead to crossed (2-crossed) modules thatare related to Kozsul complex and Andre-Quillen homology constructions for use in homotopical and homological algebra.Homotopy of crossed complex morphisms on groupoids was first introduced by Brown and Higgins in [2]. Then Martinsclearly defined and formulated the homotopy of crossed module morphisms on groups in [4]. In this study, we will definethe homotopy of crossed module morphisms on commutative algebras. Upon this, we will define a map that carries thehomotopy from simplicial algebras to crossed modules, and vice versa; as a part of the functors between them.

References[1] Arvasi Z., Porter T., Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras, TAC, 1997.

[2] Brown R., Higgins P.J., Tensor Products and Homotopies for ω-Groupoids and Crossed Complexes, Journal of Pureand Applied Algebra, 1987.

[3] Grandjean A.R., Vale M.L., 2-Modulos Cruzados en la Cohomologia de Andre-Quillen, Memorias de la Real Academiade Ciencias, 1986.

[4] Martins J.F., The Fundamental 2-Crossed Complex of a Reduced CW-Complex, Homology, Homotopy and Applica-tions, 2011.

[5] Porter T., Homology of Commutative Algebras and an Invariant of Simis and Vasconceles, Journal of Algebra, 1987.

Eskisehir Osmangazi University, Faculty of Science and Arts, Department of Mathematics and Computer Science,Eskisehir-Turkey.


127 On Algebraic Semigroup and Graph-Theoretic Propertiesof a New GraphAhmet Sinan Cevik, Eylem Guzel Karpuz and I.Naci Cangul

In this talk, firstly, we define a new graph based on the semi-direct product of some monoids, and then investigate theinterplay between the semi-direct product over monoids and the graph-theoretic properties of this product in terms of itsrelations.

References[1] A. S. Cevik, K. C. Das, I. N. Cangul, A. D. Maden, Minimality over Free Monoid Presentations, Hacettepe J. Math.

Stat., (accepted).

[2] E. G. Karpuz, K. C. Das, I. N. Cangul, A. S. Cevik, A New Graph Based on the Semi-Direct Product of Some Monoids,J. Inequalities and Appl., doi:10.1186/1029-242X-2013-118.

Ahmet Sinan Cevik: Selcuk University, Faculty of Science, Department of Mathematics, Alaaddin Keykubat Campus,Konya-Turkiye, [email protected] or [email protected]

Eylem Guzel Karpuz: Karamanoglu Mehmetbey University, Kamil Ozdag Science Faculty, Department of Mathematics,Karaman-Turkiye, [email protected]

Ismail Naci Cangul: Uludag University, Faculty of Science, Department of Mathematics, Gorukle, Bursa-Turkiye,[email protected]


128 Embeddability and Grobner-Shirshov Basis TheoryEylem Guzel Karpuz

A semigroup P embeds in a group G if there exists a monomorphism from P into G, and then a semigroup P is embeddableinto group, or is group-embeddable, if there exists some group G into which P embeds. In this talk, we discuss embeddabilityof a semigroup in a group via the Grobner-Shirshov basis theory. Then by considering braid groups, we give some examples.

Some parts of this talk have been prepared from the joint work [3].

References[1] S. I. Adjan, Defining Relations and Algorithmic Problems for Groups and Semigroups, Proceedings of the Steklov

Institute of Mathematics 85 (1966).

[2] L. A. Bokut, Y. Chen, Q. Mo, Grobner-Shirshov Bases and Embeddings of Algebras, Inter. Journal of Algebra andComp. 20(7) (2010) 875-900.

[3] E. G. Karpuz, A. S. Cevik, Jorg Koppitz, Grobner-Shirshov Bases and Embedding of a Semigroup in a Group, in prep.

Karamanoglu Mehmetbey University, Kamil Ozdag Science Faculty, Department of Mathematics, Karaman-Turkiye,[email protected]


129 An Application of Fixed Point Theorems to a Problem forthe Existence of Solutions of a Nonlinear Ordinary Differ-ential Equations of Fractional OrderMasashi Toyoda

In this talk, we consider the Cauchy problem in a class of fractional differential equations. Let 1 < α ≤ 2. We consider theCauchy problem Dα0+u(t) = p(t)tau(t)σ ,

limt→0+ u(t) = 0, limt→0+u′(t)

tα−2= (α− 1)λ

where p is continuous, a, σ, λ ∈ R with σ < 0, λ > 0 and Dα0+ is the Riemann-Liouville fractional derivative. If α = 2, thenthis problem is the problem in [8]. This is a joint work of Professor Toshiharu Kawasaki.

References[1] Z. Bai and H. Lu, Positive solutions for boundary value problem on nonlinear fractional differential equation, Journal

of Mathematical Analysis and Applications, 311 (2005), 495–505.

[2] T. Kawasaki and M. Toyoda, Existence of positive solution for the Cauchy problem for an ordinary differential equation,Nonlinear Mathematics for Uncertainly and its Applications, Advances in Intelligent and Soft Computing, 100, Springer-Verlag, Berlin and New York, 2011, 435–441.

[3] T. Kawasaki and M. Toyoda, On the existence of solutions of second order ordinary differential equations, Proceedingsof the International Symposium on Banach and Function Spaces IV, Kitakyushu, Japan, 2012, 403–413.

[4] T. Kawasaki and M. Toyoda, Positive solutions of initial value problems of negative exponent Emden-Fowler equations,Memoris of the Faculty of Engineering, Tamagawa University, 48 (2013), 25–30.

[5] T. Kawasaki and M. Toyoda, Existence of positive solutions of the Cauchy problem for a second-order differentialequation, Journal of Inequalities and Applications 2013, 2013:465 (7 November 2013).

[6] T. Kawasaki and M. Toyoda, Existence of positive solution for the Cauchy problem for an ordinary differential equation,RIMS Kokyroku (2014), No.1821, 26–32.

[7] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, InNorth-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam, 2006.

[8] J. Knezevic-Miljanovic, On the Cauchy problem for an Emden-Fowler equation, Differential Equations, 45(2009), 267–270.

Faculty of Engineering, Tamagawa University, 6-1-1 Tamagawa-gakuen Machida-shi, Tokyo, 194-8610, Japan, [email protected]


130 A Numerical Solution for Vibrations of an Axially MovingBeamDuygu Donmez Demir and Erhan Koca

The dynamic responce of an axially elastic, tensioned beam with constant velocity is considered. The equation of motionis solved by using Adomian Decomposition Method (ADM) and Method of Multiple Time Scales. We obtain displacementone at a time. Also, the comparison of (ADM) with the perturbation method for this model is presented. The computedresults are indicated numerically.

References[1] G. Adomian, Stochastic Systems, Academic Press, London, 1983

[2] A. M. Wazwaz, Partial Differantial Equations, A. A. Belkema Publishers, Tokyo, 2002,

[3] J. A. Wickert, Non-Linear Vibration of a Travelling Tensioned Beam, International Journal of Non-Linear Mechanics,27 (1992), 503-517.

[4] H. R. Oz, M. Pakdemirli, Vibrations of an Axially Moving Beam With Time-Dependent Velocity, Journal of Sound andVibration, 227(2) (1999), 239-257

[5] G. Yigit, Wave Propagation in Composite Materials With the Help of Adomian Decomposition Method, 2002

[6] I. Karagoz, Numerical Analysis and Engineering Applications, Third Edition, Nobel Publication.

[7] K. Abbaoui, Y. Cherruault, Converge of Adomians Method Applied to Differential Equations, Comp. Math. Appl., 28(1994), 103-109.

Duygu Donmez Demir: Celal Bayar University, Faculty of Art & Science, Department of Mathematics, Muradiye,Manisa-Turkiye, [email protected]

Erhan Koca: Celal Bayar University, Faculty of Art & Science, Department of Mathematics, Muradiye, Manisa-Turkiye


131 Some Principal Congruence Subgroups of the ExtendedHecke Groups and Relations with Pell-Lucas NumbersZehra Sarıgedik, Sebahattin Ikikardes and Recep Sahin

In this talk, we consider the Hecke groups H(√m) and the extended Hecke groups H(

√m) for m = 2 or 3. Firstly, we give

the generators of the principal congruence subgroups H2(√m) and H2(

√m) of H(

√m) and H(

√m), respectively. Then,

using some of these generators, we define a sequence Vk which is generalized version of the Pell-Lucas numbers sequenceQk given in [9] for the modular group, in the extended Hecke groups H(

√m) for m = 1, 2 and 3.

References[1] Hecke, E. Uber die bestimmung dirichletscher reichen durch ihre funktionalgleichungen, Math. Ann., 112, 664-699,

(1936).

[2] Lang, M. L. Normalizers of the congruence subgroups of the Hecke groups G4 and G6, J. Number Theory 90, no. 1,31–43, (2001).

[3] Sahin, R.; Bizim, O. Some subgroups of the extended Hecke groups H(λq), Acta Math. Sci., Ser. B, Engl. Ed., Vol.23,No.4, 497-502, (2003).

[4] Sahin, R.; Bizim, O.; Cangul, I. N. Commutator subgroups of the extended Hecke groups H(λq), Czechoslovak Math.J. 54(129), no. 1, 253–259, (2004).

[5] Ikikardes, S.; Sahin, R.; Cangul, I. N. Principal congruence subgroups of the Hecke groups and related results, Bull.Braz. Math. Soc. (N.S.), 40, No. 4, 479-494, (2009).

[6] Sahin, R.; Ikikardes, S.; Koruoglu, O. Extended Hecke groups H(λq) and their fundamental regions, Adv. Stud.Contemp. Math. (Kyungshang), 15, no. 1, 87–94, (2007).

[7] Cangul, I. N.; Bizim, O. Congruence subgroups of some Hecke groups, Bull. Inst. Math. Acad. Sinica, 30 (2002), no.2, 115-131.

[8] Alperin, R. C. The modular tree of Pythagoras, Amer. Math. Monthly, 112, no. 9, 807-816, (2005).

[9] Mushtaq, Q.; Hayat, U. Pell numbers, Pell-Lucas numbers and modular group, Algebra Colloq., 14, no.1, 97-102,(2007).

[10] Goldman, W. M.; Neumann, W D. Homological action of the modular group on some cubic moduli spaces, Math. Res.Lett., no. 4, 575–591, (2005).

[11] Kock, B.; Singerman, D Real Belyi theory, Q. J. Math. 58, no. 4, 463–478, (2007).

Zehra Sarıgedik: Celal Bayar University, Koprubasi Vocational High School, Koprubasi/Manisa-Turkiye, [email protected]

Sebahattin Ikikardes: Balikesir University, Faculty of Science, Department of Mathematics, Balikesir-Turkiye, [email protected]

Recep Sahin: Balikesir University, Faculty of Science, Department of Mathematics, Balikesir-Turkiye, rsahin @balike-sir.edu.tr


132 On the Metric Geometry and Regular PolyhedronsTemel Ermis and Rustem Kaya

The Platonic solids known as the regular polyhedrons, all of whose faces are congruent regular polygons, and where thesame number of faces meet at every vertex. The regular polyhedrons were first described by Plato. That is the reason whythey called as Platonic solids.

In the previous studies, hexahedron and octahedron associated to maximum and taxicab metrics, respectively. In thiswork, we find two new metrics of which unit spheres are the dodecahedron and icosahedron, and study the structure ofrelated spaces.

References[1] A. C. Thompson, Minkowski Geometry, Cambridge University Press, (1996),

[2] G. E. Martin, Transformation Geometry, Springer - Verlag New York Inc., (1987),

[3] M. Ozcan, O. Gelisgen and R. Kaya, Distance Formulae in Chinese Checker Space, International Journal of Pure andApplied Mathematics, 26-1, 35-44 (2006),

[4] O. Gelisgen and R. Kaya, On α–Distance in Three Dimensional Space, Applied Science (APPS), Vol.8, No 1. (2006),

[5] O. Gelisgen and R. Kaya, Generalization of α-distance to n-Dimensional Space, Scientific and Professional Journal ofthe Croatian Society for Geometry and Graphics (KoG), Vol.10, 33-35, (2006),

[6] O. Gelisgen and R. Kaya, The Taxicab Space Group, Acta Mathematica Hungarica, Acta Mathematica Hungarica, Vol.122, No.1-2, 187-200, (2009),

[7] S. Ekmekci, A. Bayar, O.Gelisgen and R. Kaya, On The Group of Isometries of The Plane with Generalized AbsoluteValue Metric, Rocky Mountain Journal of Mathematics, Vol.39, No.2, 591-604, (2009),

[8] R. S. Millman, G. D. Parker, Geometry, A Metric Approach with Models, Undergraduate Texts in Mathematics,Springer-Verlag, (1981).

Eskisehir Osmangazi University, Faculty of Science and Arts, Department of Mathematics and Computer Science,Eskisehir, Turkey


133 On the Addition of Collinear Points in Some PK-PlanesBasri Celik and Abdurrahman Dayioglu

In this study, we extend the addition of points which is defined in [3] for the points of the special line OU = [0, 1, 0], to thepoints of the lines [m,1,k],[1,n,p] in any PK-plane coordinated with the dual local ring of quaternion Q(ε) = Q + Qε, wherem,k and p ∈ Q(ε), n ∈ Qε. Also some geometric and algebraic properties of the addition has examined.

References[1] Baker CA, Lane ND and Lorimer JW, A coordinatization for Moufang-Klingenberg planes, Simon Stevin, 1991, 65,3–

22.

[2] Celik B. and Dayioglu A. , The collineations which act as addition and multiplication on points in a certain class ofprojective Klingenberg planes, Journal of Inequalities and Applications, 2013:193, 2013.

[3] Celik B. and Erdogan F. O. , On addition and multiplication of points in a certain class of projective Klingenbergplanes, Journal of Inequalities and Applications, 2013:230, 2013.

[4] Conway J. H. and Smith D.A., On Quaternions and Octonions, AK Peters, Massachusetts, 2003.

[5] Hughes D.R. and Piper F.C., Projective Planes, Springer, New York, 1973.

[6] Keppens D., Coordinazation of Projective Klingenberg Planes, Simon Stevin, 1988,62, 63-90.

Basri Celik: Uludag University, Faculty of Art and Science, Department of Mathematics, Gorukle, Bursa-TurkiyeAbdurrahman Dayioglu: Uludag University, Faculty of Art and Science, Department of Mathematics, Gorukle, Bursa-

Turkiye


134 Local Stability Analysis of Strogatz Model with Two De-laysSertac Erman and Ali Demir

In this talk, we consider the model of interpersonal interactions with two delays which is a direct extension of Strogatzmodel. We attempt to show stability regions of the model in various parameter spaces by using D-partition method. Thestability of model is investigated for various values of delays. We conclude that delays effect the stability of the model.

References[1] S. Strogatz, Love affairs and differential equations, Math. Mag. 65 (1) (1988) 35,

[2] S. Strogatz, Nonlinear Dynamics and Chaos, Westwiev Press, 1994,

[3] N. Bielczyk, U. Forys, T. P latkowski, Dynamical models of dyadic interactions with delay, J. Math. Sociology (2013),

[4] N. Bielczyk, M. Bodnar, U. Forys, Delay can stabilize: Love affairs dynamics, App. Math. and Comp. 219 (2012)3923-3937,

[5] A.M. Krall, Stability Techniques for Continuos Linear System, Gordon and Breach Science Publishers, London, 1967,

[6] L. E. El’sgol’ts, S. B. Norkin, Introduction to the Theory andApplication of Differential Equations with DeviatingArguments, Academic Press, London, 1973

[7] T. Insperger, G. Stepan,Semi-Discretization Stability and Engineering Applications for Time-Delay Systems, Springer,Newyork, 2011

[8] V. B. Kolmanıvskii, V. R. Nosov, Stability of Functional Differential Equations, Academic Press, London, 1986

Sertac Erman: Kocaeli University, Faculty of Science and Art, Department of Mathematics, Umuttepe, Kocaeli-Turkiye,[email protected]

Ali Demir: Kocaeli University, Faculty of Science and Art, Department of Mathematics, Umuttepe, Kocaeli-Turkiye,[email protected]


135 Weighted Statistical Convergence in Intuitionistic FuzzyNormed SpacesSelma Altundag and Esra Kamber

In this talk, we define the concepts of weighted statistical convergence,(N, pn

)statistical summability and strong

(N, pn

)-

summability in intuitionistic fuzzy normed spaces. We also establish relations between these concepts.

References[1] K.Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20 (1986), 87-96,

[2] R. Saadati, J.H. Park, Intuitionistic fuzzy euclidean normed spaces, Commun. Math. Anal., 12 (2006), 85-90,

[3] S. Vijayabalaji, N. Thillaigovindan, Y.B. Jun, Intuitionistic fuzzy n-normed linear space, Bull. Korean. Math. Soc., 44(2007), 291-308,

[4] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74,

[5] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244,

[6] C.Sencimen, S.Pehlivan, Statistical convergence in fuzzy normed linear spaces, Fuzzy sets and systems, 159 (2008),361-371,

[7] A.Alotaibi, A.M.Alroqi, Statistical convergence in a paranormed space, Journal of inequalities and applications, 39(2012), 1-6,

[8] M.Mursaleen, λ-statistical convergence, Math. Slovaca, 50 (2000), 111-115,

[9] S. Karakus, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons andFractals, 35 (2008), 763-769,

[10] S.A.Mohiuddine,Q.M.Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos,Solitons and Fractals, 42(2009), 1731-1737,

[11] V.Karakaya, N.Simsek, M.Erturk, F.Gursoy, λ-statistical convergence of seque, Journal of function spaces and appli-cations, 2012(2012), 1-14,

[12] J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43-51,

[13] M.Mursaleen, Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space,J. Comput. Appl. Math., 233 (2009), 142-149,

[14] V.Karakaya, N.Simsek, M.Erturk, F.Gursoy, Lacunary statistical convergence of sequences of functions in intuitionisticfuzzy normed space, Journ. of intelligent and fuzzy systems , 26(2014), 1289-1299,

[15] M. Sen, P. Debnath, Lacunary statistical convergence in intuitionistic fuzzy n-normed spaces, Math. and Comp.Modelling, 54 (2011), 2978-2985,

[16] S. Altundag, E. Kamber, Lacunary ∆-statistical convergence in intuitionistic fuzzy n-normed spaces, Math. and Comp.Modelling, 40 (2014), 1-12,

[17] F. Moricz, Tauberian conditions, under which statistical convergence follows from statistical summability (C, 1), J.Math. Anal. Appl., 275 (2002), 277-287,

[18] F.Moricz, C.Orhan, Tauberian conditions, under which statistical convergence follows from statistical summability byweighted means, Studia Sci.Math. Hung, 41(2004), 391-403,

[19] V. Karakaya, T.A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci., 33 (2009), 219-223,

[20] M.Mursaleen,V. Karakaya, M.Erturk, F.Gursoy, Weighted statistical convergence and its application to Korovkin typeapproximation theorem, Appl. Math. and Comput., 218 (2012), 9132-9137,

[21] C.Belen,S.A. Mohiuddine, Generalized weighted statistical convergence and application, Appl. Math.and Comput. 219(2012), 9821-9826,

[22] R.Saadati, J.H. Park, On the intuitionistic fuzzy topological spaces. , Chaos, Solitons and Fractals, 27(2006), 331-344,

[23] T.K.Samanta, I.Jebril, Finite dimensional intuitionistic fuzzy normed linear space, Int. J. Open Problems Compt.Math, 2 (2009), 574 -591,

[24] L. Hong, J.Q. Sun, Bifurcations of fuzzy nonlinear dynamical systems, Commun. Nonlinear Sci. Numer. Simul., 1(2006), 1-12,

[25] M.A.Alghamdi, A.Alotaibi,Q.M.D.Lahani , Statistical limit superior and limit inferior in intuitionistic fuzzy normedspaces Journal of inequalities and applications, 96 (2012), 1-12.

Selma Altundag: Sakarya University, Faculty of Science, Department of Mathematics, Sakarya-Turkey, [email protected]

Esra Kamber: Sakarya University, Faculty of Science, Department of Mathematics, Sakarya-Turkey, [email protected]


136 Sturm Comparison Theorems for Some Elliptic Type Equa-tions with Damping and External Forcing TermsSinem Sahiner, Emine Mısırlı and Aydın Tiryaki

After the Picone’s significant work in 1909, numerous authors extended the Picone type identity for differential equationsof various types. In this talk, we will give a Picone-type inequality for a class of some nonlinear elliptic type equations withdamping and external forcing terms, and establish Sturmian comparison theorems using the Picone-type inequality.

References[1] Adams, R. A. and Fournier, J. J. F., Sobolev Spaces, Second Edition, Academic Press, 2003,

[2] Allegretto, W. and Huang, Y. X., A Picone’s identity for the p-Laplacian and applications, Nonlinear Anal., 32, (1998),819-830,

[3] Bognar, G. and Dosly, O., The application of Picone-type identity for some nonlinear elliptic differential equations,Acta Math. Univ. Comenian. 72 (2003), 45-57,

[4] Clark, C., Swanson, C., A., Comparison theorems for elliptic differential equations , Proc. Amer. Math. Soc. 16 (1965)886-890,

[5] Hardy G. H., Littlewood J. E. and Polya G., Inequalities, Cambridge Univ. Press, 1988,

[6] Jaros, J. and Kusano, T., A Picone type identity for second order half-linear differential equations, Acta Marth. Univ.Comenian. 68 (1999), 117-121,

[7] Jaros, J., Kusano, T. and Yoshida, N., Picone-type inequalities for nonlinear elliptic equations and their applications,J. Inequal. Appl. 6 (2001), 387-404,

[8] Jaros, J., Kusano, T. and Yoshida, N., Picone-type inequalities for elliptic equations with first order terms and theirapplications, J. Inequal. Appl. (2006), 1-17,

[9] Kusano, T., Jaros, J. and Yoshida, N., A Picone-type identity and Sturmain comparison and oscillation theorems for aclass of half-linear partial differential equations of second order, Nonlinear Analysis, Theory, Methods and Applications40 (2000), 381-395,

[10] Picone M., Sui valori eccezionali di un parametro da cui dipende un’equazione differenziale lineare ordinaria del sec-ond’ordine, Ann. Scuola Norm. Sup. Pisa 11(1909), 1-141,

[11] Swanson C. A. A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611-616,

[12] Yoshida, N., Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations, NonlinearAnalysis, Theory, Methods and Applications, 71(2009) e1354-1359,

[13] Yoshida, N., A Picone identity for half-linear elliptic equations and its applications to oscillatory theory, NonlinearAnal. 71 (2009), 4935-4951.

Sinem Sahiner: Izmir University, Faculty of Arts and Sciences, Department of Mathematics and Computer Science,Izmir-Turkiye, [email protected]

Emine Mısırlı: Ege University, Faculty of Science, Department of Mathematics, Izmir-Turkiye, [email protected]ın Tiryaki: Izmir University, Faculty of Arts and Sciences, Department of Mathematics and Computer Science,

Izmir-Turkiye, [email protected]


137 A Note on Solutions of the Nonlinear Fractional Differen-tial Equations via the Extended Trial Equation MethodMeryem Odabasi and Emine Misirli

In this study, we investigate the solutions of nonlinear fractional differential equations that have many advantages in physicalsciences and dynamic systems. By using the extended trial equation method we have successfully obtained analyticalsolutions of some nonlinear fractional differential equations. The results show that extended trial equation method isan effective and powerful mathematical tool for solving nonlinear fractional differential equations arising in mathematicalphysics.

References[1] M. Dalir and M. Bashour, Applications of Fractional Calculus, Applied Mathematical Sciences 4 (2010), no. 21-24,

[2] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, 198 (1999),

[3] C. S. Liu, , A New Trial Equation Method and Its Applications, Communications in Theoretical Physics, 45 (2006),395-397,

[4] H. Bulut, H. M. Baskonus and Y. Pandir, The Modified Trial Equation Method for Fractional Wave Equation and TimeFractional Generalized Burgers Equation, Abstract and Applied Analysis, (2013), Article ID 636802,

[5] Y. Pandir, Y. Gurefe, E. Mısırlı, The Extended Trial Equation Method for Some Time Fractional Differential Equa-tions,Discrete Dynamics in Nature and Society, (2013) Article ID 491359,

[6] G. Jumarie, Modified Riemann-Liouville Derivative and Fractional Taylor Series of Nondifferentiable Functions FurtherResults, Computers and Mathematics with Applications, 51 (2006), no. 9-10, 1367-1376,

[7] Y. Gurefe, E. Misirli, A. Sonmezoglu and M. Ekici, Extended Trial Equation Method to Generalized nonlinear PartialDifferential Equations, Applied Mathematics and Computation 219 (2013), 5253-5260.

Meryem Odabasi: Ege University, Tire Kutsan Vocational School, Tire, Izmir-Turkiye, [email protected] Misirli: Ege University, Faculty of Science, Department of Mathematics, Bornova, Izmir-Turkiye, emine.misir-

[email protected]


138 On Quantum Codes Obtained From Cyclic Codes OverF2 + uF2 + u2F2 + · · ·+ umF2

Abdullah Dertli, Yasemin Cengellenmis and Senol Eren

A method to obtain self orthogonal codes over finite fields F2 is given and the parameters of quantum codes which areobtained from cyclic codes over R = F2 + uF2 + u2F2 + · · ·+ umF2 are determined.

References[1] A.R.Calderbank, E.M.Rains, P.M.Shor, N.J.A.Sloane, Quantum error correction via codes over GF (4), IEEE Trans.

Inf. Theory, 44 (1998),1369-1387.

[2] J.Qian, Quantum codes from cyclic codes over F2 + vF2, Journal of Inform.& Computational Science 10:6(2013),1715-1722.

[3] J.Qian, L.Zhang, S.Zhu, Cyclic Codes Over Fp + uFp + ...+ uk−1Fp, IEICE Trans. Fundamentals, Vol. E 88-A, No.3,2005.

[4] J.Qian, W.Ma, W.Gou, Quantum codes from cyclic codes over finite ring, Int. J. Quantum Inform., 7(2009),1277-1283.

[5] M.Mehrdad, Torsion codes Over a finite chain rings, Second Workshop on Algebra and its Applications, 2012. 19,820-823, 2006.

[6] P.W.Shor,Scheme for reducing decoherence in quantum memory, Phys. Rev. A,52(1995), 2493-2496.

[7] X.Kai,S.Zhu, Quaternary construction of quantum codes from cyclic codes over F4 + uF4, Int. J. Quantum Inform.,9(2011), 689-700.

[8] X.Yin, W.Ma, Gray map and quantum codes over the ring F2 + uF2 + u2F2, International Joint Conferences of IEEETrust Com11,2011.

[9] Y.Cengellenmis, On (1− um)−Cyclic codes over F2 + uF2 + u2F2 + · · · + umF2, Int. J. Contemp. Math. Sciences,Vol.4, 2009, no.20, 987-992.

Abdullah Dertli: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics , Samsun,Turkey, [email protected]

Yasemin Cengellenmis: Trakya University, Faculty of Arts and Sciences, Department of Mathematics, Edirne, Turkey,[email protected]

Senol Eren: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Samsun, Turkey,[email protected]


139 On Some Functions Mapping the Zeros of Ln(x) to theZeros of L

′

n(x)Nihal Yılmaz Ozgur and Oznur Oztunc

As it is well known, studying zeros of polynomials plays an increasingly important role in Mathematical research. Fibonaccipolynomials Fn (x) are defined recursively by

Fn (x) = xFn−1 (x) + Fn−2 (x) ,

by initial conditions F1 (x) = 1, F2 (x) = x. Similarly Lucas polynomials Ln (x) are defined by

Ln (x) = xLn−1 (x) + Ln−2 (x) ,

with the initial values L1 (x) = x and L2 (x) = x2 + 2 (see [2]).In this study, we give some functions which map the modulus of the zeros of Lucas polynomials to the modulus of the

zeros of the derivative of Lucas polynomials. Also we examine the roots of first order derivatives of these polynomials.

References[1] P. Filipponi, A. Horadam, Derivative sequences of Fibonacci and Lucas polynomials, Applications of Fibonacci num-

bers, Vol. 4 (Winston-Salem, NC, 1990), 99-108, Kluwer Acad. Publ., Dordrecht, 1991,

[2] P. Filipponi, A. Horadam, Second derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 31 (1993),no. 3, 194-204,

[3] M. X. He, D. Simon, P. E. Ricci, Dynamics of the zeros of Fibonacci Polynomials, Fibonacci Quarterly, 35 (1997),no.2, 160-168,

[4] M. X. He, P. E. Ricci, D. Simon, Numerical results on the zeros of generalized Fibonacci Polynomials, Calcolo, 34(1998), no.1-4, 25-40,

[5] V. E. Hoggat, M. Bicknell, Generalized Fibonacci Polynomials, Fibonacci Quart. 11 (1973), no. 5, 457-465,

[6] V. E. Hoggat, M. Bicknell, Roots of Fibonacci Polynomials, Fibonacci Quart. 11 (1973), no. 3, 271-274,

[7] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley 2001,

[8] Y. Yuan, Z. Wenpeng, Some identities involving the Fibonacci Polynomials, Fibonacci Quart. 40 (2002), no. 4, 314-318,

[9] J. Wang, On the k th derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 33 (1995), no. 2,174-178,

[10] C. Zhou, On the k th-order derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 34 (1996), no.5, 394-408.

Nihal Yılmaz Ozgur: Balıkesir University, Department of Mathematics, 10145 Balıkesir, Turkiye, [email protected]

Oznur Oztunc: Balıkesir University, 10145 Balıkesir, Turkiye, [email protected] authors are supported by the Scientific Research Projects Unit of Balıkesir University under the project number

2013/02.


140 Finite Blaschke Products and R-Bonacci PolynomialsNihal Yılmaz Ozgur, Oznur Oztunc and Sumeyra Ucar

A Blaschke product of degree n is a function defined by

B(z) = β

n−1∏j=1

z − aj1− ajz

where |β| = 1 and aj are in the unit disc. We know that every Blaschke product B, B(0) = 0 degree n, is associated witha unique Poncelet curve, B identifies the vertices of the n−gon.

In this study, we give some examples of Poncelet curves of finite Blaschke products using the zeros of the derivatives ofthe r−Bonacci polynomials. In these cases the Poncelet curves are precisely n−ellipses.

References[1] U. Daepp, P. Gorkin and R. Mortini, Ellipses and finite Blaschke products, Amer. Math. Monthly 109 (2002), no. 9,

785-795,

[2] U. Daepp, P. Gorkin, K. Voss, Poncelet’s theorem, Sendov’s conjecture, and Blaschke products, J. Math. Anal. Appl.365 (2010), no. 1, 93-102,

[3] M. Frantz, How conics govern Mobius transformations, Amer. Math. Monthly 111 (2004), no. 9, 779-790,

[4] T. Koshy, Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics (New York). Wiley-Interscience, New York, 2001,

[5] N. Yılmaz Ozgur, Finite Blaschke Products and Circles that Pass Through the Origin, Bull. Math. Anal. Appl. 3(2011), no. 3, 64-72,

[6] N. Yılmaz Ozgur, Some Geometric Properties of finite Blaschke Products, Proceedings of the Conference RIGA 2011,(2011), 239-246,

[7] M. Fujimura, Inscribed Ellipses and Blaschke Products, Comput. Methods Funct. Theory 2013,

[8] H. W. Gau, P. Y. Wu, Numerical Range and Poncelet Property, Taiwanese J. Math. 7 (2003), no 2, 173-193.

[9] M. Bicknell, V.E. Hoggatt, Roots of Fibonacci polynomials, Fibonacci Quarterly, 11, (1973), 271–274,

[10] M. Bicknell, V.E. Hoggatt Generalized Fibonacci polynomials, Fibonacci Quarterly, 16, (1978), 300–303,

[11] M. X. He, P. E. Ricci and D. Simon, Numerical results on the zeros of generalized Fibonacci polynomials, Calcolo, 34,(1997), 25–40,

[12] M. X. He, D. Simon, P. E. Ricci, Dynamics of the zeros Fibonacci Polynomials, Fibonacci Quarterly, 35 no.2, (1997),160-168.

Nihal Yılmaz Ozgur: Balıkesir University, Department of Mathematics, 10145 Balıkesir, Turkiye, [email protected]

Oznur Oztunc: Balıkesir University, 10145 Balıkesir, Turkiye, [email protected] Ucar: Balıkesir University, Department of Mathematics, 10145 Balıkesir, Turkiye, sumeyraucar@balikesir.

edu.tr


141 Convergence of Nonlinear Singular Integral Operators tothe Borel Differentiable FunctionsHarun Karsli and Ismail U.Tiryaki

In this paper convolution type nonlinear singular integral operators of the form

Tλ(f ;x) =

b∫a

Kλ(t− x, f(t)) dt ,

where < a, b > is an arbitrary interval in R, λ ∈ Λ, f ∈ L1 < a, b > and Kλ is a family of kernels satisfying suitableproperties. We give some approximation results about the concergence of the operators Tλ to right, left and symmetricBorel differentiable functions.

We note that our results are an extention of the classical ones, namely, the results dealing with the linear singularintegral operators [9] and Poisson integrals [10].

References[1] R. Taberski, Singular integrals depending on two parameters, Rocznicki Polskiego towarzystwa matematycznego, Seria

I. Prace matematyczne, VII, (1962), 173-179.

[2] P.L. Butzer and R.J. Nessel, Fourier Analysis and Approximation, V.1, Academic Press, New York, London, 1971.

[3] C. Bardaro, J. Musielak, G. Vinti, Nonlinear Integral Operators and Applications, De Gruyter Series in NonlinearAnalysis and Applications, Vol. 9, xii + 201 pp., 2003.

[4] E. Ibikli, Approximation of Borel derivatives of functions by singular integrals. Trans. Acad. Sci. Azerb. Ser. Phys.-Tech.Math. Sci. 21 (2001), no. 4, Math. Mech., 72–76, 238.

[5] T. Ikegami, On Poisson integrals. Proc. Japan Acad. 37 1961 14–17.

Abant Izzet Baysal University, karsli [email protected], [email protected]


142 Regularization of an Abstract Class of Ill-Posed ProblemsDjezzar Salah and Benmerai Romaissa

In this talk, we present an abstract class of ill-posed problems described by a differential equation with a self-adjointunbounded operator coefficient on a Hilbert space. The class under study is regularized using a new modified quasi-boundary value method to obtain an approximate family of well-posed problems. As a result of this regularization, anapproximate family of regularized solutions is obtained. Moreover, some results concerning the stabilty estimates for theseregularized solutions as well as some convergences results are provided.

References[1] Ames, K. A., Payne, L. E., Schaefer, P. W., Energy and pointwwise bounds in some non-standard parabolic problems.

Proc. Roy. Soc. Edinburgh Sect. A 134, No.1, 1-9, 2004.

[2] Clark, G. W., Oppenheimer, S. F., Quasireversibility Methods for Non-Well-Posed Problems, Electronic Journal ofDifferential Equations, No. 8, 1-9, 1994.

[3] M. Denech and S. Djezzar, (2006), ”A modified quasi-boundary value method for a class of abstract parabolic ill-posedproblems” Boundary-Value Problems, Volume 2006. Article ID 37524, 8 pages.

[4] S. Djezzar and N. Teniou, (2011),.”Improved regularization method for backward Cauchy problems associated withcontinuous spectrum operator” International Journal of Differential Equations, Volume 2011, Article ID 93125, 11pages.

[5] Lettes, R. and Lions, J. L., Methode de Quasi-Reversibilit et Applications, Dunond, Paris, 1967.

[6] Payne, L. E., Some general remarks on improperly posed problems for partial differential equations, ”Symposium onNon-Well-Posed Problems and Logarithmic Convexity”, Lecture Notes in Mathematics, 316, 1-30, Springer Verlag,Berlin, 1973.

[7] Showalter, R. E., The final value problem for evolution equations, J. Math. Anal. Appl., 47, 563-572, 1974.

Djezzar Salah: University of Constantine 1, Faculty of Exact Sciences, Department of Mathematics, Constantine,Algeria, [email protected]

Benmerai Romaissa: University of Constantine 1, Faculty of Exact Sciences, Department of Mathematics, Constantine,Algeria, [email protected]


143 Decompositions of Soft ContinuityAhu Acıkgoz and Nihal Tas

In this talk, we introduce soft θ - open, soft θ - preopen, soft θ - semiopen, soft θ - β - open and soft θ - α - open setsin soft topological spaces and show the relationships between defined new soft sets and other soft sets using diagram. Weinvestigate some properties of these soft sets. Also we define the concepts of θ - pre - soft continuity, θ - β - soft continuity,θ(A,E) - soft continuity, θpre - B - soft continuity and θβ - B - soft continuity. Finally, we obtain decompositions of softcontinuity.

References[1] M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl.,

57 (2009) 1547-1553,

[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96,

[3] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Trans. System Man Cybernet, 23(2) (1993) 610-614,

[4] S. Hussain and B. Ahmad, Some properties of soft topological space, Comput. Math. Appl., 62 (2011) 4058-4067,

[5] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. ABD El-Latif, γ - operation and decompositions of someforms of soft continuity in soft topological spaces, Ann. Fuzzy Math. Inform. 7(2) (2014) 181-196,

[6] P. K. Maji, R. Biswas and A. R. Roy, Intuitionistic fuzzy soft sets, The J. of F. Math. 9 (2001) 677-692,

[7] P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, The J. of F. Math. 9 (2001) 589-602,

[8] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555-562,

[9] D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999) 19-31,

[10] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011) 1786-1799,

[11] L. A. Zadeh, Fuzzy sets, Infor. and Control 8 (1965) 338-353,

[12] I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform. 3(2012) 171-185.

Ahu Acıkgoz: Department of Mathematics, Balikesir University, 10145 Balikesir, Turkey, [email protected] Tas: Department of Mathematics, Balikesir University, 10145 Balikesir, Turkey, [email protected]


144 Lacunary Statistical Convergence of Double Sequences inTopological GroupsEkrem Savas

By X, we will denote an abelian topological Hausdorff group, written additively, which satisfies the first axiom of countability.The double sequence θ = (kr, ls) is called double lacunary if there exist two increasing of integers such that

k0 = 0, hr = kr − kk−1 →∞ as r →∞

andl0 = 0, hs = ls − ls−1 →∞ as s→∞.

Notations: kr,s = krls, hr,s = hrhs,θ is determine by Ir = (k) : kr−1 < k ≤ kr, Is = (l) : ls−1 < l ≤ ls,Ir,s = (k, l) : kr−1 < k ≤ kr & ls−1 < l ≤ ls, qr = kr

kr−1, qs = ls

ls−1, and qr,s = qr qs. We will denote the set of all double

lacunary sequences by Nθr,s .In 2005, R. F. Patterson and E. Savas [1] studied double lacunary statistically convergence by giving the definition forcomplex sequences as follows:

Tanım 144.1. Let θ be a double lacunary sequence; the double number sequence x is st2θ − convergent to L provided thatfor every ε > 0,

P − limr,s

1

hr,s|(k, l) ∈ Ir,s : |x(k, l)− L| ≥ ε| = 0.

In this case write st2θ − limx = L or x(k, l)→ L(S2θ ).

In this paper we introduce and study lacunary statistical convergence for double sequences in topological groups andwe shall also present some inclusion theorems.

References[1] R. F. Patterson and Ekrem Savas, Lacunary statistical convergence of double sequences,J. Math. Commun., 10 (2000),

55-61.

Istanbul Commerce University, Department of Mathematics, Uskudar, Istanbul, TURKEY, [email protected]


145 On Fuzzy Pseudometric SpacesElif Aydın and Servet Kutukcu

In this paper, we introduce two classifications in fuzzy pseudometric spaces and examine relationships between themillustrating with examples.

References[1] A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 64(3)(1994), 395 - 399,

[2] B. Schweizer, A. Sklar, Statistical Metric Spaces, Pacific Journal of Mathematics, 10(1)(1960), 313-334,

[3] L. A. Zadeh, Fuzzy Sets, Information and Control, 8(3)(1965), 338-353,

[4] M. Grabiec, Fixed Points in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 27(1)(1989), 385-389,

[5] M. A. Erceg, Metric Spaces in Fuzzy Set Theory, Journal Mathematical Analysis Applications, 69 (1979), 205-230,

[6] O. Kaleva and S. Seikkala, On Fuzzy Metric Spaces, Fuzzy Sets and Systems 12 (1984), 215-229,

[7] Z. Deng, Fuzzy Pseudometric Spaces, Journal Mathematical Analysis Applications, 86(1982), 74-95.

Elif Aydın: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit, Samsun-Turkey, elif [email protected]

Servet Kutukcu: Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit,Samsun-Turkey, [email protected]


146 On Fixed Points of Extended Hecke GroupsBilal Demir and Ozden Koruoglu

Hecke groups H(λq) are Fuchsian groups of the first kind and generated by two linear fractional transformations; T (z) =−(z)−1 and S(z) = −(z + λq)−1, where λq = 2 cos(π/q), q ≥ 3 integer[1]. Then H(λq) has a presentation;

H(λq) =< T, S : T 2 = Sq = I >' C2 ∗ CqThe extended Hecke groups have been defined in [7], [8] by adding the reflection R(z) = 1/z to the generators of Hecke

groups H(λq).H(λq) =< T, S,R : T 2 = Sq = R2 = I, TR = RT, SR = RSq−1 >' D2 ∗C2 Dq

Let W (z) be an arbitrary element of H(λq). The solutions of the equation W (z) = z are called fixed points of theelement W (z).Each transformation in H(λq) has at most two fixed points except for identity. In extended Hecke groupscase a whole circle can be fixed by a transformation.

In this talk we give some results about fixed points of the elements in extended Hecke groups H(λq).

References[1] Hecke E, Uber die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann., 112 (1936), 664-699.

[2] Cangul IN, Normal Subgroups and Elements of H′(λq), Tr. J. of Mathematics 23 (1999), 251–256.

[3] Cangul IN, The Group Structure of H(λq), Tr. J. of Mathematics 20 (1996), 203–207.

[4] Cangul IN and Singerman D, Normal Subgroups of Hecke Groups and Regular Maps, Math. Proc. Camb. Phil. Soc,.123 (1998), 59-74.

[5] Ikikardes S, Sahin R and Cangul IN, Principal congruence subgroups of the Hecke groups and related results, Bull. Braz.Math. Soc. (N.S.) 40, No. 4, 479-494 (2009).

[6] Sahin R and Koruoglu O, Commutator subgroups of the power subgroups of some Hecke groups, Ramanujan J. 24 (2011),no. 2, 151–159.

[7] Sahin R and Bizim O, Some Subgroups of Extended Hecke Groups H(λq), Actua Math. Sci. 23 (4) (2003), 497-502.

[8] Sahin R, Bizim O and Cangul IN, Commutator Subgroups of the Extended Hecke Groups, Czech. Math..28 (2004),253-259.

Bilal Demir: Balikesir University Necatibey Faculty of Education Department of Mathematics Education, Balıkesir-Turkiye, [email protected]

Ozden Koruoglu: Balikesir University Necatibey Faculty of Education Department of Primary Mathematics Education,Balıkesir-Turkiye, [email protected]

This work was supported by the Commission of Scientific Research Projects of Balikesir University, Project number2014/99.


147 New Lagrangian Forms of Modified Emden Equation byJacobi MethodGulden Gun Polat and Teoman Ozer

The aim of the our work determination of Lagrangians and first integrals of modified Emden equation with respect to theJacobi method. This novel approach enable to us to obtain Jacobi last multiplier’s by means of known Lie symmetries ofgoverning equation. Ratio of two Jacobi last multiplier corresponds to first integral. Based on this fact we present differentfirst integrals of modified Emden equation. Furthermore some Hamiltonians and explicit solutions are derived.

References[1] G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989

[2] L.V. Ovsiannikov, Group Analysis of Differential Equations, Moscow, Nauka, 1978

[3] N.H. Ibragimov, editor. CRC Handbook of Lie Group Analysis of Differential Equations vols, I-III, 1994

[4] P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, 1986

[5] T. Ozer, Symmetry group classification for one-dimensional elastodynamics problems in nonlocal elasticity, MechanicsResearch Communications, 30(6), 539-546, 2003

[6] T. Ozer, On symmetry group properties and general similarity forms of the Benney equations in the Lagrangianvariables, Journal of Computational and Applied Mathematics, 169 (2), 297-313, 2004

[7] T. Ozer, Symmetry group classification for two-dimensional elastodynamics problems in nonlocal elasticity, Interna-tional Journal of Engineering Science, 41(18), 2193-2211, 2003

[8] M. N. Nucci, K. M. Tamizhmani, Using an old method of Jacobi to derive Lagrangians: a nonlinear dynamical systemwith variable coefficients, arXiv: 0807.2791v1, 2008

[9] M. N. Nucci, P.G.L. Leach, An old method of Jacobi to find Lagrangians, J. Nonlinear Msth. Phys. 16, 431-441, 2009

[10] M. N. Nucci, P.G.L. Leach, The Jacobi Last Multiplier and its applications in mechanics, Physica scripta, 78, 2008

[11] A. Bhuvaneswari, R. Kraenkel, M. Senthilvelan, Application of the lambda-symmetries approach and time independentintegral of the modified Emden equation, Nonlinear Analysis: Real World Applications. 13(2), 1102-1114, 2012

[12] E. Yasar, M. Reis, Application of Jacobi Method and integrating factors to a class of Painleve-Gambier equations, J.Phys. A: Math. Theor. 43, 2010

[13] M. N. Nucci, P.G.L. Leach, Jacobi’s last multiplier and symmetries for the Kepler problem plus a lineal story, J. Phys.A: Math. Gen. 37, 7743-7753, 2004

[14] M. N. Nucci, Jacobi last multiplier and Lie symmetries: a novel application of an old relationship, J. Nonlinear Msth.Phys. 12, 284-304, 2005

[15] M. N. Nucci, P.G.L. Leach, Lagrangians galore, J. Math. Phys. 48, 123350, 2007

Gulden Gun Polat: Istanbul Technical University, Faculty of Science and Letters, Department of Mathematics, 34469Maslak, Istanbul-Turkey

Teoman Ozer: Istanbul Technical University, Division of Mechanics, Faculty of Civil Engineering, 34469 Maslak,Istanbul-Turkey, [email protected]

Corresponding author: Teoman Ozer.


148 Fixed Point Theorems for ψ-Contractive Mappings on Mod-ular SpaceEkber Girgin and Mahpeyker Ozturk

We introduce ψρ-contractive mappings, then we establish fixed point theorem for such mappings on modular spaces. As aconsequences of this theorems, we obtain fixed point theorems on modular space with a graph. In addition, we present anexample to illustrate the usability of the main results.

References[1] H. Nakano, Modulared Semi-Ordered Linear Spaces, In Tokyo Math Book Ser, (1), Maruzen Co., Tokyo (1950).

[2] S. Koshi, T. Shimogaki, On F-norms of quasi-modular spaces, J Fac Sci Hokkaido Univ Ser I, (15) (3-4), (1961),202-218.

[3] S. Yamamuro, On conjugate spaces of Nakano spaces, Trans Amer Math Soc., (90), (1959), 291-311.

[4] WAJ. Luxemburg, Banach function spaces, Thesis, Delft, Inst of Techn Asser, The Netherlands, (1955).

[5] T. Musielak, W. Orlicz, On Modular spaces, Studia Math, (18), (1959), 49-65.

[6] C.M. Chen, Fixed Point Theorems for Weak ψ-Contractive Mappings in Ordered Metric Spaces, Journal of APpliedMathematics, (2012), (2012), 10, Article ID 756453.

[7] H. K. NAshine, Z. Golubovic, Z. Kadelburg, Modified ψ-contractive mappings in ordered metric spaces with applica-tions, Fixed Point Theory and Applications, (2013), (2013), doi: 10.1186/1687-1812-2012-203.

[8] S. Chandok, S. Dinu, Common Fixed Points for Weak ψ-Contractive Mappings in Ordered Metric Spaces with Appli-cations, Abstract and Applied Analsis, (2013), (2013), 7, Article ID 879084.

[9] J. Jachymski, The contraction principle for mappings on a metric space endowed with a graph, Proc. Amer. Math.Soc., 136(2008), 1359-1373.

[10] M. Abbas, T. Nazir, Common fixed point of a power graphic contraction pair in partial metric spaces endowed with agraph, Fixed Point Theory and Applications, (2013), (2013), 20.

[11] M. Ozturk, E. Girgin, On Some Fixed Point Theorems with ϕ-Contractions in Cone Metric Spaces Involving a Graph,Int. Journal of Math. Analysis., 7(2013), 3109-3117.

[12] M. Ozturk, E. Girgin, On some fixed-point theorems for ψ-contraction on metric space involving a graph, Journal ofInequalities and Applications, 2014 (2014):39, doi: 10.1186/1029-242X-2014-39.

[13] M. Ozturk, M. Abbas, E. Girgin, Fixed Points of Mappings Satisfying Contractive Condition of Integral Type inModular Spaces endowed with a Graph, Submitted

Mahpeyker Ozturk: Department of Mathematics, Sakarya University, 54187, Sakarya, Turkey, [email protected]

Ekber Girgin: Department of Mathematics, Sakarya University, 54187, Sakarya, Turkey, [email protected]


149 Convexity and Schur Convexity on New MeansV.Lokesha, U.K.Misra and Sandeep Kumar

In this talk, we discuss some Convexity and Schur harmonic convexity of the Gnan mean, HP-mean and its dual formsare discussed. One can go further investigations on the geometrical aspects of Convexities.

References[1] P. S. Bullen, Handbook of Means and Their Inequalities, Kluwer Acad. Publ., Dordrecht, 2003.

[2] V. Lokesha, Zhi-Hua Zhang and K. M. Nagaraja, Gnan mean for two variables, Far East Journal of Mathematics, 31(2)(2008), 263-272.

[3] V. Lokesh, K. M. Nagaraja, B. Naveen Kumar and Y-.D. Wu, Shur convexity of Gnan mean for positive arguments,Notes on Number Theory and Discrete Mathematics, 17(4) (2011), 37-41.

[4] K. M. Nagaraja and P. Siva Kota Reddy, Logarithmic convexity and concavity of some Double sequences, ScientiaMagna, 7(2) (2011), 78-81.

[5] B. Naveenkumar, Sandeepkumar, V. Lokesha and K. M. Nagaraja, Ratio of difference of means and its convexity,International eJournsl Mathematics and Engineeting, 2(2) (2011), 932-936

[6] H. N. Shi, Y. M. Jiang and W. D. Jiang, Schur-Geometrically concavity of Gini Mean, Comp. Math. Appl., 57(2009),266-274.

[7] R. Webster, Convexity, Oxford University Press, Oxford, New York, Tokyo, 1994.

[8] X. M. Zang, Geometrically Convex Functions, AnHui University Press, Hefei, 2004(in Chi- nese).

V.Lokesha: Department of Mathematics, V. S.K. University, Bellary, India, [email protected]: Department of Mathematics, Berhampur University, Berhampur, Orissa, IndiaSandeep Kumar: Department of Mathematics, Acharya Institute of technology, Bangalore, [email protected] First author thankful to Authorities of the V. S. K. University, Bellary


150 On Radial Signed GraphsGurunath Rao Vaidya, P.S.K.Reddy and V.Lokesha

In this paper we introduced a new notion radial signed graph of a signed graph and its properties are obtained. Also,we obtained the structural characterization of radial signed graphs. Further, we presented some switching equivalentcharacterizations.

Gurunath Rao Vaidya: Department of Mathematics, Acharya Institute of Graduate Studies, Bangalore-560 107, India,[email protected]

P.S.K. Reddy: Department of Mathematics, S.I.T, Tumkur, India, [email protected]. Lokesha: Department of Mathematics, V.S.K. University, Bellary, India, [email protected] first author thankful to The Chairman, Acharaya Instiutes, Bangalore


151 Delta and Nabla Discrete Fractional Gruss Type InequalityA.Feza Guvenilir

Properties of the discrete fractional calculus in the sense of a backward and forward difference are introduced and developed.Here, we prove a more general version of the Gruss type inequality for the delta and nabla fractional case. An example ofour main result is given.

Ankara University, Ankara, [email protected]


152 On Tame Extensions and Residual Transcendental Exten-sions of a Valuation with rankv = nBurcu Ozturk and Figen Oke

Let (K, v1) be a henselian valued field, vi be a valuation of residue field kvi and v = v1 v2/circ... vn be a composite ofvaluations v1, v2, ..., vn for i = 2, ..., n . Let L/K be a finite extension, z1 be an extension of v1 to L , zi be an extension ofvi to the residue field kzi and z = z1 z2 ... zn be an extension of v to L which is a composite of valuations z1, z2, ..., znfor i = 2, ...n .

In this paper it is shown that if (L, z)/(K, v)) is a tame extension then (L, z1)/(K, v1)) and (kzi−1 , zi−1)/(kvi−1 , vi))are tame extensions for i = 2, ..., n .

Also in this paper a residual transcendental extension w = w1 w2 ... wn of v to K(x) is studied where w1 is aresidual transcendental extension of v1 to the rational function field K(x) defined by minimal pair (a1, δ1) and wi be aresidual transcendental extension of vi to the residue field kwi−1 defined by minimal pair (ai, δi) for i = 2, ...n .

References[1] O. Endler, Valuation Theory , Springer-Verlag, 1972

[2] O. Zariski, P. Samuel, Commutative Algebra Volume II, D. Von. Nostrand, Princeton, 1960

[3] N. Popescu, C. Vraciu,On the Extension of a valuation on a field K to K(x) .-II, Rend. Sem. Mat. Univ. Padova, Vol96, (1996), 1-14

[4] N. Popescu, A. Zaharescu, On the Structure of the Irreducible Polynomials over Local Fields, J. Number Theory, 52,No.1, (1995), 98-118

[5] V. Alexandru, N. Popescu, A. Zaharescu, A Theorem of Characterization of Residual Transcendental Extensions of aValuation, J. Math. Kyoto Univ., 28-4, (1988), 579-592

[6] K. Aghigh, S. K. Khanduja, On Chains Associated with Elements Algebraic over a Henselian Valued Field, AlgebraColloquim, 12:4 (2005), 607-616

[7] K. Aghigh, S. K. Khanduja, A Note on Tame Fields, Valuation Theory and its Applications, Vol II, Fields InstituteCommunications, 33, 1-6, 2003B.

[8] Ozturk, F. OKE, On Residual Transcendental Extensions of a Valuation with rankv=2, Selcuk J. Appl. Math. Vol.12No.2 . pp 111-117, 2011B.

[9] Ozturk, F. OKE, Some Constants and Tame Extensions According to a Valuation of a Field with rankv=2, Proc.Jangjeon Math. Soc., 15, No. 4, 477- 482, 2012

Burcu Ozturk: Trakya University, Faculty of Science, Department of Mathematics, Edirne-Turkiye, [email protected]

Figen Oke: Trakya University, Faculty of Science, Department of Mathematics, Edirne-Turkiye, [email protected]


153 Time Series Forecasting with Grey ModellingSeval Ene and Nursel Ozturk

Time series is a collection of data points measured over a period of time. Time series forecasting defines the process ofpredicting future value based on previously observed data by using a mathematical model. Time series forecasting methodshave a wide application field as in engineering, social science, economics etc. However in some real world applications, wehave limited and uncertain data. Grey models forecast the future values of a time series based on most recent data other thanclassical forecasting models. Grey system theory was first introduced by Deng (1982). The theory is an interdisciplinaryscientific research area. In this paper grey modeling is proposed for forecasting time series characterized as uncertain andsmall sized. To test the performance of the proposed grey model, data sets from literature are used. Obtained resultsshowed the performance and applicability of the model particularly for forecasting data sets with small size and uncertainty.

References[1] [1] J. Deng, Introduction to grey system theory, J. Grey Syst., 1 (1989), 1-24.

[2] E. Kayacan, B. Uluta, O. Kaynak, Grey system theory-based models in time series prediction. Expert Syst. Appl., 37(2010), 1784-1789.

[3] E. Kse, S. Erol, . Temiz, Grey system approach for EOQ models. Sigma, 28 (2010), 298-309.

[4] X. Wang, L. Qi, C. Chen, J.Tang, M. Jiang, Grey system theory based prediction for topic trend on Internet. Eng.Appl. Artif. Intel., 29 (2014), 191-200.

[5] A.W.L. Yao, S.C. Chi, J.H. Chen, An improved Grey-based approach for electricity demand forecasting, Electr. Pow.Syst. Res., 67 (2003), 217-224.

[6] M. Shah, Fuzzy based trend mapping and forecasting for time series data, Expert Syst. Appl., 39 (2012), 6351-6358.

Seval Ene: Uludag University, Faculty of Engineering, Industrial Engineering Department, Gorukle Campus, 16059,Bursa, Turkey, [email protected]

Nursel Ozturk: Uludag University, Faculty of Engineering, Industrial Engineering, Department, Gorukle Campus, 16059,Bursa, Turkey, [email protected]


154 Periodic Solution of Predator-Prey Dynamic Systems withBeddington-DeAngelis Type Functional Response and Im-pulsesAyse Feza Guvenilir, Billur Kaymakcalan and Neslihan Nes-

liye Pelen

We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response and impulses onTime Scales. For this special case we try to find under which conditions the system has periodic solution. Our study ismainly based on continuation theorem in coincidence degree theory. This study will also give beneficial results for continuousand discrete case.

References[1] D. Bainov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Pitman Mono-

graphs and Surveys in Pure and Applied Mathematics, Longman Scientific and Technical, Harlow, UK, vol. 66,1993.

[2] J. R. Beddington Mutual interference between parasites or predators and its effect on searching efficency Journal ofAnimal Ecology,vol. 44, pp. 331340, 1975.

[3] Martin Bohner,Meng Fan,Jimin Zhang. Existence of periodic solutions in predatorprey and competition dynamic sys-tems. Nonlinear Analysis: RealWorld Applications 7 (2006) 1193 1204.

[4] D. L. DeAngelis, R. A. Goldstein, and R. V. ONeill, A model for trophic interaction, Ecology, vol.56, pp. 881892, 1975.

[5] M. Fan, S. Agarwal, Periodic solutions for a class of discrete time competition systems, Nonlinear Stud. 9 (3) (2002)249261.

[6] M. Fan, K. Wang, Global periodic solutions of a generalized n-species GilpinAyala competition model, Comput. Math.Appl. 40 (1011) (2000) 11411151.

[7] M. Fan, K.Wang, Periodicity in a delayed ratio-dependent predatorprey system, J. Math. Anal. Appl. 262 (1) (2001)179190.

[8] M. Fan, Q.Wang, Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predatorpreysystems, Discrete Contin.Dynam. Syst. Ser. B 4 (3) (2004) 563574.

[9] H.F. Huo, Periodic solutions for a semi-ratio-dependent predatorprey system with functional responses, Appl. Math.Lett. 18 (2005) 313320.

[10] Y.K. Li, Periodic solutions of a periodic delay predatorprey system, Proc. Amer. Math. Soc. 127 (5) (1999) 13311335.

[11] A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific Series on Nonlinear Science.Series A:Monographs and Treatises,World Scientific, River Edge,NJ, USA,vol. 14 , 1995.

[12] S. Tang, Y. Xiao, L. Chen, and R. A. Cheke, Integrated pest management models and their dynamical behaviour,Bulletin of Mathematical Biology, vol. 67, no. 1, pp. 115135, 2005.

[13] Q. Wang, M. Fan, K. Wang, Dynamics of a class of nonautonomous semi-ratio-dependent predatorprey systems withfunctional responses,J. Math. Anal. Appl. 278 (2) (2003) 443471.

[14] Peiguang Wang. Boundary Value Problems for First Order Impulsive Difference Equations. International Journal ofDifference Equations. Volume 1 Number 2 (2006), pp. 249259.

[15] Weibing Wang, Jianhua Shen,Juan J. NietoPermanence and Periodic Solution of Predator-Prey System with HollingType Functional Response and Impulses Discrete Dynamics in Nature and Society Volume 2007, Article ID 81756, 15pages.

[16] Chunjin Wei and Lansun Chen Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Re-sponse and Impulsive State Feedback Control Journal of Applied Mathematics Volume 2012, 2012, 17 pages.

[17] Z. Xiang, Y. Li, and X. Song, Dynamic analysis of a pest management SEI model with saturation incidence concerningimpulsive control strategy, Nonlinear Analysis, vol. 10, no. 4, pp. 23352345, 2009.

[18] R. Xu, M.A.J. Chaplain, F.A. Davidson, Periodic solutions for a predatorprey model with Holling-type functionalresponse and time delays, Appl. Math. Comput. 161 (2) (2005) 637654.

Ayse Feza Guvenilir: Ankara University, Faculty of Science, Department of Mathematics, Ankara, Turkey, [email protected], http://math.science.ankara.edu.tr/akademik/afguvenilir.html

Billur Kaymakcalan: Cankaya University, Department of Mathematics and Computer Science, 06810, Ankara, Turkey,[email protected], http://mcs.cankaya.edu.tr/ billur

Neslihan Nesliye Pelen: Middle East Technical University, Department of Mathematics, Ankara, Turkey, [email protected]


155 Approximation Properties of Kantorovich-Stancu Type Gen-eralization of q-Bernstein-Schurer-Chlodowsky Operators onUnbounded DomainTuba Vedi and Mehmet Ali Ozarslan

In this paper, we introduce the Kantorovich-Stancu type generalization of q-Bernstein-Chlodowsky operators on the un-bounded domain. We should note that this generalization include various kind of operators which are not introduced earlier.We calculate the error of approximation of these operators by using modulus of continuity and Lipschitz-type functionals.Finally, we give generalization of the operators and investigate its approximations.

References[1] Agrawal, PN, Gupta, V, Kumar, SA: On a q-analogue of Bernstein-Schurer-Stancu operators, Applied Mathematics

and Computation, 219, 7754-7764 (2013).

[2] Barbosu, D: Schurer-Stancu Type Operators, Babes-Bolyai Math., XLVIII (3), 31-35 (2003).

[3] Barbosu, D: A survey on the approximation properties of Schurer-Stancu operators, Carpatian J. Math., 20, 1-5 (2004).

[4] Buyukyazıcı, I: On the approximation properties of two dimensional q-Bernstein-Chlodowsky polynomials, Math Com-mun., 14 (2), 255-269 (2009).

[5] Buyukyazıcı, I, Sharma, H: Approximation properties of two-dimensional q-Bernstein-Chlodowsky-Durrmeyer opera-tors, Numer. Funct. Anal. Optim., 33 (2), 1351-1371

(2012).

[6] Ibikli, E: On Stancu type generalization of Bernstein-Chlodowsky polynomials, Mathematica, 42 (65), 37-43 (2000).

[7] Chlodowsky, I: Sur le development des fonctions defines dans un interval infini en series de polynomes de M. S.Bernstein, Compositio Math., 4, 380-393 (1937).

[8] DeVore, RA, Lorentz, GG: Constructive Approximation, Springer-Verlag, Berlin (1993).

[9] Gadjiev, AD: The convergence problem for a sequence of positive linear operators on unbounded sets and theoremsanalogues to that of P. P. Korovkin, Dokl. Akad. Nauk SSSR 218 (5), English Translation in Soviet Math. Dokl. 15(5), (1974).

[10] Ibikli, E: Approximation by Bernstein-Chlodowsky polynomials, Hacettepe Journal of Mathematics and Statics, 32,1-5 (2003).

[11] Kac, V, Cheung, P: Quantum Calculus, Springer, 2002.

[12] Karslı, H, Gupta, V: Some approximation properties of q-Chlodowsky operators, Applied Mathematics and Computa-tion, 195, 220-229 (2008).

[13] Muraru, CV: Note on q-Bernstein-Schurer operators, Babes-Bolyaj Math., 56, 489-495 (2011).

[14] Ozarslan, MA: q-Szasz Schurer operators, Miscolc Mathematical Notes, 12, 225-235 (2011).

[15] Ozarslan, MA, Vedi, T: q- Bernstein-Schurer-Kantorovich Operators, J. of Ineq. and Appl., 2013, 2013:444doi:10.1186/1029-242X-2013-444.

[16] Phillips, GM: On Generalized Bernstein polynomials, Numerical analysis, World Sci. Publ., River Edge, 98, 263-269(1996).

[17] Phillips, GM: Interpolation and Approximation by Polynomials, Newyork, (2003).

[18] Schurer, F: Linear Positive Operators in Approximation Theory, Math. Inst., Techn. Univ. Delf Report, 1962.

[19] Stancu, DD: Asupra unei generalizari a polinoamelor lui Bernstein [ On generalization of the Bernstein polynomials],Studia Univ. Babes-Bolyai Ser. Math.-Phys., 14 (2), 31-45 (1969).

[20] Vedi, T, Ozarslan, MA: Some Properties of q-Bernstein-Schurer operators, J. Applied Functional Analysis, 8 (1), 45-53(2013).

[21] Vedi, T, Ozarslan, MA: Chlodowky variant of q-Bernstein-Schurer-Stancu operators, J. of Ineq. and Appl., 2014,10.1186/1029-242X-2014-189.

Tuba Vedi: Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey, [email protected]

Mehmet Ali Ozarslan: Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey, [email protected]


156 Use of Golden Section in MusicSumeyye Bakım

In this study the relationship of Fibocacci Sequence and Golden Ratio with music questioned. Pre acceptances on thestudies applied to the chosen examples of some European art music/multi- vocal composers up to now have been discussedwithin the framework of mathematical and musical.

References[1] Koshy, T., 2001, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publication, Canada.

[2] Lehmann, I., Posamentier, Alfred S., 2007, The (Fabulous) Fibonacci Numbers, Alfred S. Posamentier, Ingmar,Lehmann, Prometheus Books, 2007, 271-291.

[3] Power, T., 2001, J. S. Bach and the Divine Proportion, Doctoral Thesis, Department of Music, Duke University.

KTO Karatay Universite, [email protected]


157 On Analysis of Mathews-Lakshmanan Oscillator Equationvia Nonlocal Transformation and Lagrangian-HamiltonianDescriptionOzlem Orhan and Teoman Ozer

In this study, we consider Mathews-Lakshmanan Oscillator Equation which possesses exact periodic solution, exhibitingthe characteristic amplitude-dependent frequency of nonlinear oscillator in spite of the sinusoidal nature of the solution ofequation. Mathews-Lakshmanan Oscillator Equation has a natural generalization in three dimensions and these systemscan be also quantized exhibiting many interesting features and can be interpreted as an oscillator constrained to moveon a three-sphere. Firstly, we examine the first integral in the form A(t, x)x + B(t, x) and then, we consider other firstintegrals of the equation via this finding λ-symmetry. Using the coefficients of the equation, we characterize this equationthat can be linearized by means of nonlocal transformation that is called Sundman transformation. In addition, the timeindependent integrals for Mathews-Lakshmanan Oscillator Equation are obtained by using modified Prelle-Singer procedure.We demonstrate that the equation is integrable by these first integrals. Further, the Lagrangian- Hamiltonian forms areinvestigated using this time-independent first integral. Finally, we compare results obtained by two different methods.

References[1] G.W. Bluman and S. Kumei, Symmetries and Differential Equations, 1989,

[2] P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, 1993,

[3] N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations vols. I-III, CRC Press, 1994.

[4] H. Stephani, Differential Equations: Their Solutions Using Symmetries, Cambridge University Press, Cambridge,1989.

[5] C. Muriel, and J. L. Romero, Nonlocal transformation of linearization of second-Order Ordinary Differential Equations,Journal of Physics A: Mathematical and Theoretical 43 (2010), 434025,

[6] C. Muriel, and J. L. Romero, Second-Order Ordinary Differential Equations and First Integrals of The Form A(t, x)x+B(t, x), Journal of Nonlinear Mathematical Physics 16(2009), 209-222,

[6] T. Ozer, Symmetry group classification for two-dimensional elastodynamics problems in nonlocal elasticity, Interna-tional Journal of Engineering Science 41(18)(2003), 2193-2211,

[8] L. G. S. Duarte, S. E. S. Duarte, L. A. C. P. da Mota and J. E. F. Skea, Solving second-order ordinary differentialequations by extending the Prelle-Singer method, J. Phys. A:Math. Gen. 34(2001), 3015-3024.

[9] E. Yasar, λ-symmetries, nonlocal transformations and first integrals to a class of Painleve-Gambier equations, Mathe-matical Methods in the Applied Sciences 13 (2012), 684-692,13 (2012), 684-692,

[10] Ajey K. Tiwari, S. N. PANDEY, M. Senthilvelan and M. Lakshmanan, Classification of Lie point symmetries forquadratic Lienard type equation x+f(x)x2+g(x)=0, Journal of Mathematical Physics, 54 (2013), 053506,

[11] V. K. Chandrasekar, M. Senthilvelan and M. Lakshmanan, On the Lagrangian and Hamiltonian description of thedamped linear harmonic oscillator, Journal of Mathematical Physics, 48 (2007), 032701.

Ozlem Orhan: Istanbul Technical University, Faculty of Science and Letters, Department of Mathematics Engineering,34469 Maslak, Istanbul-Turkiye, [email protected]

Teoman Ozer: Istanbul Technical University, Division of Mechanics, Faculty of Civil Engineering, 34469 Maslak,Istanbul-Turkiye, [email protected]


158 On Singularities of the Galilean Spherical Darboux RuledSurface of a Space Curve in the Pseudo-Galilean Space G1

3

Tevfik Sahin and Murteza Yılmaz

In this paper, we study the singularity theory in pseudo-Galilean space, a special type of Cayley-Klein spaces. In particular,we investigate the singularities of pseudo-Galilean height functions intrinsically related to the Frenet frame along a curveembedded into pseudo-Galilean space. We also establish relationships between singularities of discriminant, bifurcation setsof the function, and geometric invariants under the action of pseudo-Galilean group of curves in pseudo-Galilean space.

References[1] Arnol’d, V.I., Gusein-Zade, S.M. and Varchenko, A.N. Singularities of Differentiable Maps vol. I (Birkhauser, 1986).

[2] Bruce, J.W. On Singularities, envelopes and elementary differential geometry, Math.Proc.Cambridge Phil.Soc. 89,43-48, 1981.

[3] Bruce, J.W. and Giblin, P.J. Generic geometry, Amer.Math.Monthly. 90, 529-561, 1983.

[4] Bruce, J.W. and Giblin, P.J. Curves and Singularities, second edition (Cambridge Univ.Press, 1992).

[5] Che, M.G., Jiang, Y. and Pei, D. The hyperbolic Darboux image and rektifying Gaussian surface of nonlightlike curvein Minkowski 3-space, Journal of Math. Research & Exposition. 28, 651-658, 2008.

[6] Divjak, B. Geometrija psudogalilejevih prostora, Ph.D. Thesis, (University of Zagreb, 1997).

[7] Divjak, B. and Sipus, Z. M. Some special surfaces in the pseudo-Galilean space, Acta Math. Hungar. 118(3), 209-226,2008.

[8] Cox, D., Little, J. and O’shea, D. Ideals,varieties, and algorithms. Second edition. (New York Springer, 1977).

[9] Casse, R. Projective geometry on introduction (Oxford Univ. Press, 2006).

[10] Erjavec, Z. and Divjak, B. The general solution of the Frenet system of differential equations for curves in the pseudo-Galilean space G1

3 , Mathematical Communications. 2, 143-147, 1997.

[11] Izumiya, S., Katsumi, H. and Yamasaki, T. The Rectifying developable and the spherical darboux image of a spacecurve, Geometry and topology of caustics ’98 – Banach Center Publications. 50, 137-149, 1999.

[12] Izumiya, S. and Takeuchi, N. Generic properties of helices and Bertrand curves, J.Geom. 74, 97-109, 2002.

[13] Izumiya, S. and Sano, T. Generic affine differential geometry of space curves, Proc.Royal soc. Edinburgh. 128A,301-314, 1998.

[14] Molnar, E. The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom.38, 261-288, 1997.

[15] Mond, D. Singularities of the tangent developable surface of a space curve, Quart. J. Math. Oxford. 40, 79-91, 1989.

[16] Montaldi, J.A. Surfaces in 3-space and their contact with circles, J.Differential Geom. 23(2), 109-126, 1986.

[17] O’Neill, B. Elementary Differential Geometry (Academic Press, Inc., 1966).

[18] Pei, D. and Sano, T. The focal developable and the binormal indicatrix of a nonlightlike curve in Minkowski 3-space,Tokyo J. Math. 23(1), 211-225, 2000.

[19] Roschel, O. Die Geometrie des Galileischen Raumes, Habilitationssch (Inst. fur Mat . und Angew. Geometrie, 1984).

[20] Sahin, T. and Yılmaz, M. On singularities of the Galilean spherical darboux ruled surface of a space curve in G3,Ukranian Math. Journal, 62(10), 1597-1610, 2011.

[21] Sahin, T. and Yılmaz, M. The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space, ActaMath. Hungar. 132(1-2) 154-167, 2011.

[22] Sipus, Z. M. and Divjak, B. Surface of constant curvature in the pseudo-Galilean space, International J. of Math. andMath. Sci. Vol 2012, 28 p., 2012.

[23] Yaglom, I.M. A Simple Non-Euclidean Geometry and Physical Basis (Sprınger-Verlag Newyork, 1979).

Tevfik Sahin: Amasya University, Faculty of Sciences and Arts, Department of Mathematics, Amasya-Turkey, [email protected]

Murteza Yılmaz: TOBB University of Economics & Technology, [email protected]


159 Existence of Positive Solutions for Second Order Semiposi-tone Boundary Value Problems on the Half-LineF.Serap Topal and Gulsah Yeni

In this talk, we aim to establish a sufficient condition for the existence of positive solution for semipositone singular Sturm-Liouville boundary value problems on the half-line of an unbounded time scale by using Guo-Krasnosels’ kii fixed pointtheorem.

F.Serap Topal: Ege University, Faculty of Science, Department of Mathematics, [email protected] Yeni: Missouri University of Science and Technology, Department of Mathematics and Statistics, [email protected]


160 Some Congruent Number FamiliesRefik Keskin and Ummugulsum Ogut

In this study, we give some congruent number families concerning generalized Lucas sequences (Vn).

References[1] J. Coates, Congruent Number Problem, Pure and Appl. Math. Quaterly, Volume1, Number1, 14-27, 2005.

[2] J. S. Chahal, Congruent Numbers and Elliptic Curves, Amer. Math. Monthly, Vol. 113, No. 4, 308-317, 2006.

[3] K. Conrad, The Congruent Number Problem, http://www.thehcmr.org/issue2 2/congruent number.pdf.

[4] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Second Edition, Springer Verlag, 1993.

[5] A. Lozano-Robledo, Elliptic Curves, Modular Forms and their L-Functions, Student Mathematical Library, 2010.

[6] S. Zhang, Congruent Numbers and Heegner Points, Asia Pacific Newsletter, Vol 3 No 2, 12-15, 2013.

[7] A. Wiles, Modular Elliptic Curves and Fermat’s Last Theorem, Ann. of Math. (2) 141, 443–551, 1995.

[8] R. Keskin, M. G. Duman, Positive integer solutions of some Pell equations (submitted).

[9] F. Izadi, Congruent numbers via the Pell equations and its analogous counterpart, arxiv: 1004.0261v4[math,HO] 30Dec. 2010.

[10] P. Serf, Congruent numbers and elliptic curves, Computational Number Theory, Walter de Gruyter and Co., Berlin,New York, 227-238, 1991.

[11] G. Kramarz, All congruent numbers less than 2000, Mathematische Annalen, Berlin, Heidelberg, 337-340, 1968.

[12] R. Alter, T.B. Curtz, A note on congruent numbers, Math. Comp.,303-305, 1974.

Refik Keskin: Sakarya University, Faculty of Sciences and Arts, Department of Mathematics, Sakarya-Turkiye, [email protected]

Ummugulsum Ogut: Sakarya University, Faculty of Sciences and Arts, Department of Mathematics, Sakarya-Turkiye,[email protected]


161 On Some Fourth-Order Diophantine EquationsMerve Guney Duman and Refik Keskin

Let k ≥ 3 be an odd integer. In this paper, we show that the equations x4 − (k2 − 4)y2 = 4(k − 2), x4 − (k2 − 4)y2 =−4(k + 2), x2 − (k2 − 4)y4 = −4(k + 2) and x4 − kx2y + y2 = −(k + 2) have no positive integer solutions. Moreover, weshow that if k ≡ 1(mod8), then the equation x4 − (k2 − 4)y2 = −4(k− 2) has no positive integer solutions, if k ≡ 3(mod8),then the equation x4 − (k2 − 4)y2 = 4(k+ 2) has no positive integer solutions and if k2 − 4 is a squarefree integer, then theequations x4 − kx2y + y2 = −(k − 2)(k2 − 4) and x4 − kx2y + y2 = (k + 2)(k2 − 4) have no positive integer solutions. Inaddition, we define all positive integer solutions of the some fourth-order diophantine equations.

References[1] LeVeque J. W., Topics in Number Theory, Volume 1 and 2, Dover Publications 2002,

[2] Lucas E., Theorie des Fonctions, Numeriques Simplement Periodiques, American Journal of Mathematics, 1,2, 184-196,1878,

[3] Ribenboim P., McDaniel W. L., The square terms in Lucas sequences, J. Number Theory, 58, 104-123, 1996,

[4] Ribenboim P., My Numbers, My Friends, Springer-Verlag New York, Inc., 2000,

[5] Kalman D., Mena R., The Fibonacci Numbers exposed, Mathematics Magazine 76, 167-181, 2003,

[6] McDaniel W. L., Diophantine Representation of Lucas Sequences, The Fibonacci Quarterly 33, 58-63, 1995,

[7] Siar Z., Keskin R., Some new identities concerning generalized Fibonacci and Lucas numbers, Hacettepe Journal ofMathematics and Statistics, 42, 3, 211-222, 2013,

[8] Siar Z., Keskin R., The Square Terms in Generalized Lucas Sequences, Mathematika 60, 1, 85-100, 2014,

[9] Keskin R., G. Duman M., Positive integer solutions of some second order Diophantine equations (submitted),

[10] Keskin R., Solutions of Some Quadratics Diophantine Equations, Computers and Mathematics With Applications, 60,8, 2225-2230, 2010,

[11] Melham R., Conics Which Characterize Certain Lucas Sequences, The Fibonacci Quarterly 35, 248-251, 1997,

[12] Nagell T., Introduction to Number Theory, Chelsea Publishing Company, New York, 1981,

[13] Robinowitz S., Algorithmic Manipulation of Fibonacci Identities, in: Application of Fibonacci Numbers, vol. 6, KluwerAcademic Pub, Dordrect, The Netherlands, 389-408, 1996,

[14] Jones J.P., Representation of Solutions of Pell equations Using Lucas Sequences, Acta Academia Pead. Agr., SectioMathematicae, 30, 75-86, 2003,

[15] Keskin R., Yosma Z., On Fibonacci and Lucas numbers of the form cx2, Journal of Integer Sequences, Vol 14, 1-12,2011,

[16] Keskin R., Generalized Fibonacci and Lucas Numbers of the form wx2 and wx2±1, Bulletin of the Korean MathematicalSociety (accepted),

[17] Nakamula K., Petho A., Squares in Binary Recurrence Sequences, In: ”Number Theory”, Walter de Gruyter GmbH&Co., Berlin-New York, 1998, pp. 409–421,

[18] Mignotte M., Petho A., Sur les carres dans certaines suites de Lucas, Journal de Theorie des Nombres de Bordeaux, 5no. 2 (1993), 333–341,

[19] Cohn J. H. E., Lucas and Fib. Numbers Some Diophantine Equation, Proc. Glasgow Math. assoc., 7(1965), 24-28.

Merve Guney Duman: Sakarya University, Faculty of Science and Arts, Department of Mathematics, Adapazarı,Sakarya-Turkiye [email protected]

Refik Keskin: Sakarya University, Faculty of Sciences and Arts, Department of Mathematics, Sakarya-Turkiye, [email protected]


162 Characteristic Subspaces of Finite Rank OperatorsMohamed Najib Ellouze

Recently, Uffe Haagerup and Hanne Schultz proved in [1] that for any operator T inM, whereM is a factor of type II1 suchthat the spectral measure of Brown is not concentrated in a singleton (cf. [2]), has a non-trivial closed T -hyperinvariant

subspace, constructed by spectral projectors of the limit A := limn→+∞(T ∗nTn)12n (cf. [3]). In this paper, we prove the

existence of this limit for all finite rank operators, and we define the corresponding characteristic subspaces.

References[1] U.Haagerup and H. Schultz. Invariant subspaces for operators in a general II1-factor, Publications mathA c©matiques

July 2009, Vol 109, Issue 1, pp 19-111.

[2] L.G.Brown, Lidskii’s theorem in the type II Case, Pitman Res. Notes in Math. Ser 123, Longman Sci. Tech 1986, pp1-35.

[3] R.V.Kadison and J.R.Ringrose, Fundamentals of the Theory of Operator Algebras, Vol 1 . Academic Press, New York,1983.

Sfax University, Faculty of Sciences, Departement of Mathematics, Route de Soukra 3018 Sfax BP 802, Tunisia, [email protected]


163 Fixed Point Theory in WC-Banach AlgebrasBilel Mefteh

In this paper, we will prove some fixed point theorems for the sum and the product of nonlinear weakly sequentiallycontinuous operators acting on a WC-Banach algebra. Our results improve and correct some results of the recent paper ofBanas and Taoudi [1], and extend some several earlier works using the condition P” where [1] is the following reference:

References[1] J. Banas, M. A. Taoudi, Fixed points and solutions of operator equations for the weak topology in Banach algebras,

Taiwanese Journal of Mathematics. DOI: 10.11650/tjm.18.2014.3860, (2014).

Department of Mathematics, Faculty of Sciences of Sfax , Road Soukra Km 3.5, B.P 1172-3018, Sfax - Tunisia,[email protected]


164 Oscillation and Nonoscillation Criteria for Second OrderGeneralized Difference EquationsYasar Bolat

In this talk, we discuss some new oscilation and nonoscillation criteria for second order nonlinear difference equationwith generalized difference operators which generalize and improve some results in the literatures. Also, some examplesillustrating the results are included.

References[1] Y. Bolat and O. Akın, Oscillation criteria for higher order half linear delay difference equations involving generalized

difference, Mathematica Slovaca, in press.

[2] S. Chen and L. H. Erbe, Riccati Techniques and Discrete Oscillations, J. Math. Anal. Appl., 142, 468-487 (1989).

[3] X.Z. He, Oscillatory and Asymptotic Behavior of Second Order Nonlinear Difference Equations, J. Math. Anal. Appl.,175(2), 482–498 (1993).

[4] M. M. S. Manuel and at all, Asymptotic behavior of solutions of generalized nonlinear difference equations of secondorder, Communications in Differential and Difference quations, 3 (1), 13-21, (2012).

[5] M. M. S. Manuel and at all, Oscillation, nonoscillation and growth of solutions of generalized second order nonlinearα- difference equations, Global Journal of Mathematical Science: Theory and Pratical, 4(3), 211-225 (2012).

[6] J. Popenda, Oscillation and nonoscillation theorems for second order difference equations, J. Math. Anal. Appl., 123,34-38 (1987).

[7] Z. Szafranski and B. Szmanda, Oscillatory Behavior of Difference Equations of Second Order, J. Math. Anal. Appl.,150, 414-424 (1990).

[8] M-C. Tan and E-H. Yang, Oscillation and nonoscillation theorems for second order difference equations, J. Math. Anal.Appl., 276, 239-247, (2002).

[9] E. Thandapani, Oscillation theorems for perturbed nonlinear second order difference equations, Computers & Mathe-matics with Applications, 28(1–3), 309–316 (1994).

[10] E. Thandapani, Oscillation criteria for a second order damped difference equation, Applied Mathematics Letters, 8(1),1–6 (1995).

[11] E. Thandapani, Tamilnadu, Oscillation theorems for a second order damped nonlinear difference equation, CzechoslovakMathematical Journal, 45 (120), 327-335 (1995).

[12] P.J. Y. Wong, Oscillation theorems and existence of positive monotone solutions for second order nonlinear differenceequations, Mathematical and Computer Modelling, 21 (3), 63–84 (1995).

[13] B.G. Zhang, Oscillation and Asymptotic Behavior of Second Order Difference Equations, J. Math. Anal. Appl., 173(1),58–68 (1993).

Kastamonu University, Faculty of Science and Arts, Department of Mathematics, 37100-Kastamonu-Turkey, [email protected]


165 On Generalizations of Some Inequalities Containing Dia-mond-Alpha Integrals and ApplicationsBillur Kaymakcalan

We present a survey of some generalizations and refinements of the Opial, Hlder, Hardy and Constantin type Inequalitiescontaining the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. Somerelated applications are also given.

Cankaya University, Department of Mathematics and Computer Science, Ankara, Turkey, [email protected]


166 On Reciprocity Law of the Y (h, k) Sums Associated withPDE’s of the Three-Term Polynomial RelationsElif Cetin, Yilmaz Simsek and Ismail Naci Cangul

By using PDE’s of the three-term polynomial relations, we find a new finite sum which is related to the Hardy-Berndt sumsand the Simsek’s sum Y (h, k). By using PDEs, we give another poof of reciprocity law of this sum. Our method is differentfrom that of Simsek’s (On Analytic properties and character analogs of Hardy Sums, Taiwanese J. Math. 13 (1) (2009),253-268 ). We also give some relations and remarks on these sums.

References[1] Apostol, T. M., Modular functions and Dirichlet Series in Number Theory, Springer-Verlag(1976).

[2] Apostol, T. M., and Vu, T. H., Elementary Proofs of Berndt’s Reciprocity Laws, Pasific J. Math. 98 (1982), 17-23.

[3] Beck, M., Geometric proofs of polynomial reciprocity laws of Carlitz, Berndt, and Dieter, M. Beck, in Diophantineanalysis and related fields 2006, Sem. Math. Sci. 35, Keio Univ., Yokohama, 2006, pp. 11–18.

[4] Berndt, B. C., Analytic Eisenstein Series, Theta-functions, and Series relations in the spirit of Ramanujan, J.Reine Angew. Math. 303/304(1978), 332-150.

[5] Berndt, B., and Dieter, U., Sums involving the greatest integer function and Riemann Stieltwes integration, J.Reine Angew. Math. 337, 208-220 (1982).

[6] Berndt, B. C., and Goldberg, L. A., Analytic Properties of Arithmetic Sums arising in the theory of the classicalTheta-functions, SIAM., J. Math. Anal. 15(1984),. 143-150.

[7] M. Can and V. Kurt, CHARACTER ANALOGUES OF CERTAIN HARDY-BERNDT SUMS, International Journalof Number Theory 10 (3) (2014), 737–762.

[8] Carlitz, L., Some polynomials associated with Dedekind Sums, Acta Math. Sci. Hungar, 26 (1975), 311-319.

[9] E. Cetin, Y. Simsek and I. N. Cangul, Some special finite sums related to PDE’s of the three-term polynomials relationsand their applications, preprint.

[10] Goldberg, L. A., Transformation of Theta-functions and analogues of Dedekind sums, Thesis, University of IllinoisUrbana(1981).

[11] Hardy, G. H., On certain series of discontinues functions, connected with the modular functions, Quart. J. Math.36(1905), pp. 93-123 (= Collected papers, vol.IV, pp. 362-392. Clarendon Press Oxford (1969)).

[12] Pettet, M. R., and Sitaramachandraro, R., Three-Term relations for Hardy sums, J. Number Theory 25(1989),328-339.

[13] Simsek, Y., On Generalized Hardy Sums s5(h, k), Ukrainian Math. J., 56(10) (2004), 1434-1440.

[14] Simsek, Y., Theorems on Three-Term Relations for Hardy sums, Turkish J. Math. 22(1998), 153-162.

[15] Simsek, Y., A note on Dedekind sums, Bull. Cal. Math. Soci. 85(1993) 567-572.

[16] Simsek, Y., On Analytic properties and character analogs of Hardy Sums, Taiwanese J. Math. 13 (1) (2009), 253-268.

[17] Sitaramachandrarao, R., Dedekind and Hardy sums, Acta Arith. XLVIII (1978).

Elif Cetin: Uludag University, Faculty of Science, Department of Mathematics, Gorukle, Bursa-Turkey, Celal BayarUniversity, Faculty of Arts and Science, Department of Mathematics, Manisa, Turkey, [email protected]

Yilmaz Simsek: Akdeniz University, Faculty of Science, Department of Mathematics, Antalya, Turkey, ysimsek @akd-eniz.edu.tr

Ismail Naci Cangul: Uludag University, Faculty of Science, Department of Mathematics, Gorukle, Bursa-Turkey, [email protected]

The authors are supported by the research fund of Akdeniz University and Uludag University.


167 Permutation Method for a Class of Singularly PerturbedDiscrete Systems with Time-DelayTahia Zerizer

Discrete-time systems with state delay have strong background in engineering applications. However, the singularly per-turbed discrete system with time-delay has not been fully investigated. In this paper, we develop the perturbation methodfor a class of linear singularly perturbed discrete systems with time delay. Convergent algorithms are provided showing thesteps of the method.

Scientific Classes, Faculty of Sciences, Jazan University, Jazan, Saudi Arabia, [email protected]


168 Existence of Minimal and Maximal Solutions for Quasilin-ear Elliptic Equation with Nonlocal Boundary Conditionson Time-ScalesMohammed Derhab and Mohammed Nehari

The purpose of this work is the construction of minimal and maximal solutions for a class of second order quasilinear ellipticequation subject to nonlocal boundary conditions. More specifically, we consider the following nonlinear boundary valueproblem −

(ϕp(u∆))∆

= f (x, u) , in (a, b)T ,u (a)− a0u∆ (a) = g0 (u) ,u (σ (b)) + a1u∆ (σ (b)) = g1 (u) ,

where p > 1, ϕp (y) = |y|p−2 y,(ϕp(u∆))∆

is the one-dimensional p−Laplacian, f : [a, b]T × R → R is a rd-continuous

function, gi : Crd([a, b]T

)× Crd

([a, b]T

)→ R (i = 0 and 1) are rd-continuous and a0 and a1 are a positive real numbers.

Mohammed Derhab: Department of Mathematics, Faculty of Sciences, University Abou-Bekr Belkaid Tlemcen, B.P.119,Tlemcen, 13000, Algeria, [email protected]

Mohammed Nehari: Department of Mathematics, Faculty of Sciences, University Ibn Khaldoun Tiaret, Algeria, ne-hari [email protected]


169 Application of Filled Function Method in Chemical Con-trol of PestsAhmet Sahiner, Meryem Oztop, Gulden Kapusuz and Ozan Demi-

rozer

Rhodococcus perornatus (Cockerell & Parrott) is an important pest on oil-bearing rose(Rosa damascena Mill.) and themethidation has been used for a long time in order to control of the pest. As usual determining the effects of plant protectionproducts on the organism is very important in pest management practices. In this study, the effect of the MethidathionE.C. 426 g/l on R. perornatus is modeled by using fuzzy logic approach. To obtain the maximum effect on the pest, howlong the pesticide should be applied is determined by using the Filled Function Method.

References[1] Zadeh LA. 1965. Fuzzy sets, Inform. Control, 8, 338-353.

[2] Sakawa M. 1993. Fuzzy sets and interactive multi objective optimiztion, With 1 IBM-PC floppy disk, Appl. Info. T.,(Plenum Press).

[3] Kosko B. 1992. Neural network and Fuzzy systems. A dynamical systems approach to machine intelligence With 1IBM-PC floppy disk (Prentice Hall, Inc.-1992).

[4] Mamdani EH. 1974. Application of fuzzy algorithms for simple dynamic plant, Proc. IEE 121, 1585-1588.

[5] Saltan M, Saltan S, Sahiner A. 2007. Fuzzy logic modeling of deflection behavior aganist dynamic loading in flexiblepavements, Construction and Building Materials, 21, 1406-1414.

[6] Mamdani EH, Assilian S. 1975. An experiment in linguistic synthesis with a fuzzy logic controller, International Journalof Man-Machine Studies 7 (1), 1-13.

[7] Ge RP. 1990. A filled function method for finding global minimizer of a function os several variables, Mathematicalprogramming, 46, 191-204.

[8] Ge RP. 1987. The theory of filled function method for finding global minimizer of a nonlinearly constrained Minimizationproblem, J. Comput. Math. 5 (1), 1-9.

[9] Ge RP. 1990. The globally convexized filled functions for global optimzation, Appl. Math. Comput. 35, 131-158.

[10] Liu X. 2002. Several filled functions with mitigators, Appl. Math. Comput. 133 (2002), 375-387.

[11] Liu, X. 2001. Finding global minima eith computable filled function, J. Global Optim. 19,151-161.

[12] Sahiner A, Gokkaya H. 2012. An application of filled function method to the hardness property of Fe-Mn Binary Alloys,Uncertainty Modeling in Knowledge Engineering and Decision Making, 10th International FLINS Conference, Istanbul.

Ahmet Sahiner: Suleyman Demirel University, Department of Mathematics, Isparta, Turkiye, [email protected]

Meryem Oztop: Suleyman Demirel University, Department of Mathematics, Isparta, Turkiye, [email protected] Kapusuz: Suleyman Demirel University, Department of Mathematics, Isparta, Turkiye, guldenkapusuz92

@gmail.comOzan Demirozer: Suleyman Demirel University, Department of Plant Protection, Isparta, Turkiye, ozandemirozer@sdu.

edu.tr


170 A New Approach to the Filled Function Method for Non-smooth ProblemsNurullah Yilmaz and Ahmet Sahiner

The filled function method (FFM) is one of the effective method for smooth problems. Recently, studies on FFM have beenconcentrated on non-smooth problems. In this study, we present a new algorithm which hold some properties of the FFM,to find the global minimizer of the non-smooth but continuous functions.

References[1] W. X. Wang, Y. L.Shang, L. S. Zhang, Y. Zhang, Global optimization of non-smooth unconstrained problems with

filled functions, Optim. Lett. 7, 435-446, (2013).

[2] W. X. Wang, Y. L.Shang, Y. Zhang, Finding Global Minima with a Novel Filled Function for Non-smooth Uncon-strained Optimisation, Int. J. Syst. Sci. 4 , 707-714, (2012).

[3] Z.Y. Wu, H. W. J.Lee, L.S. Zhang, X. M. Yang, A Novel Filled Function Method and Quasi-Filled Function Methodfor Global Optimization, Comput. Optim. Appl., 34, 246-272 (2005).

[4] W.X. Wang, Y.L. Shang, Y. Zhang, A Filled Function Approach for Nonsmooth Constrained Global Optimization,Math. Probl. Eng., 2010, Article ID 310391, 9 pages (2010).

[5] Z. Xu,H.X. Huang, P. M. Pardalos, C. X. Xu,Filled functions for unconstrained global optimization, J. Glob. Opt., 20,49-65 (2001).

[6] Y. Zhang, L.Zhang, Y. Xu, New filled functions for non-smooth global optimization, App. Math. Model., 33, 3114-3129(2009).

[7] N. Karmitsa, Nonsmooth Optimization in 30 minutes, 2013,web-page: http://napsu.karmitsa.fi/nso/ , Erisim:15.04.2014.

[8] Y. Lin, Y. Yang, L. Zhang, A Novel Filled Function Method for Global Optimization, J. Korean Math. Soc. 47, 6,1253-1267 (2010).

[9] N. Mahdavi-Amiri, R. Yousefpour, An Effective Optimization Algorithm for Locally Nonconvex Lipschitz FunctionsBased on Mollifier Subgradients, Bull. Iranian Math. Soc., 31 (1),171-198, (2011).

[10] A. Sahiner, H. Gokkaya, T. Yigit, A new filled function for non-smooth global optimization, AIP Conf. Proc. 1479,972-974 (2012).

Nurullah Yilmaz: Suleyman Demirel University, Department of Mathematics, Cunur, Isparta, Turkiye, [email protected]

Ahmet Sahiner: Suleyman Demirel University, Department of Mathematics, Cunur, Isparta, Turkiye, [email protected]


171 Determining of the Achievement of Students by UsingClassical and Modern Optimization TechniquesAhmet Sahiner and Raziye Akbay

The purpose of this study is to investigate effects of sleeping hours and study time to students’ achievement and find outin which case minimum and maximum achievement level occurs by using global optimization methods.

References[1] E. H. Mamdani, Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis, IEEE Trans.

Computers, 26(12):1182-1191, 1977.

[2] F. Esragh and E.H. Mamdani, A general approach to linguistic approximation,Fuzzy Reasoning and Its Applications,Academic Press,1981.

[3] Mamdani, E.H., 1974. Application of fuzzy algorithms for simple dynamic plant. Proc. IEE 121, 1585.1588.

[4] Sahiner, A., Gokkaya, H., Ucar, Nazım., 2013. Nonlinear Modelling of the Layer Microhardnes of Fe-Mn Binory Allays,Journal of Balkan Tribological Association, (2013) 4,508-519.

[5] Sahiner, A., Uney I., Gurbuz M. F., An Application of Fuzzy Logic in Entomology: Estimating the Egg Productionand Opening of Pimpla Turianellae L., IWBCMS-2013 Procoeding Book, 323-332.

[6] Saltan M., Saltan S., Sahiner, A., 2007. Fuzzy logic modeling of de.ection behavior aganist dynamic loading in. exiblepavements, Construction and Building Materials, 21, 1406-1414.

[7] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans.Syst., Man, Cybern, 15:116.132, 1985.

[8] Zadeh , L., A., 1965. Fuzzy Sets, Inf. Control, 8,338-353.

[9] Zadeh, L., A., 1978.Fuzzy Sets as a Basis for a Theory of Posibility.Fuzzy Sets Syst, 1, 3-28.

[10] Zadeh,L., The consept of a linguistic variable and its application to approximate reasoning I, Information Sciences,8(3), 199-249, (1975)

[11] Karagoz S.,Zulfikar H.,Kalaycı T.,2014.ogrenme surecine iliskin degerlendirmeler ve fuzzy karar verme teknigi ile surecedair bir uygulama 56-71.

[12] Ari E., Vatansever F.,2009,Bulanık mantık tabanlı mesleki yonlendirme vocatıonal guidance based on fuzzy logic,

Ahmet Sahiner: Suleyman Demirel University, Faculty of Art and Science, Department of Mathematics, Isparta, Turkiye,[email protected]

Raziye Akbay: Suleyman Demirel University, Faculty of Art and Science, Department of Mathematics, Isparta, Turkiye,[email protected]


172 Fuzzy Logic Approach to an UH-1 Helicopter Fuel Con-sumption and Calculation of Power ProblemAhmet Sahiner and Reyhane Ercan

The fuel consumption of UH-1 Helicopter is related with air temperature,altitude,speed and weight. Before the flight,pilots spend many times to calculate estimated fuel consumption. Aim of this work is shorten the time of pilots spend forcalculation and find the fuel consumption which can be minimum in which conditions by using fuzzy logic in filled function.

References[1] Allahviranloo, T., 2005. Successive Over Relaxation Iterative Method for Fuzzy System of Linear Equations. ApplMath

Comput, 162(1), 189-196.

[2] B. Kosko, Fuzzy thinking: The new science of fuzzy logic, Hyperion, New York, 1992.

[3] Elsalamony, G., 2006. A note on fuzzy neighbourhood base spaces. Fuzzy Sets Syst,

157(20), 2725-2738.

[4] E. H. Mamdani, Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis, IEEE Trans.Computers, 26(12):1182-1191, 1977.

[5] F. Esragh and E.H. Mamdani, A general approach to linguistic approximation,Fuzzy Reasoning and Its Applications,Academic Press,1981.

[6] Mamdani, E.H., 1974. Application of fuzzy algorithms for simple dynamic plant. Proc. IEE 121, 1585.1588.

[8] Sahiner, A., Gokkaya, H., Ucar, Nazım., 2013. Nonlinear Modelling of the Layer Microhardnes of Fe-Mn Binory Allays,Journal of Balkan Tribological Association, (2013) 4,508-519.

[9] Sahiner, A., Uney I., Gurbuz M. F., An Application of Fuzzy Logic in Entomology: Estimating the Egg Productionand Opening of Pimpla Turianellae L., IWBCMS-2013 Procoeding Book, 323-332.

[10] Saltan M., Saltan S., Sahiner, A., 2007. Fuzzy logic modeling of de.ection behavior aganist dynamic loading in. exiblepavements, Construction and Building Materials, 21, 1406-1414.

[11] UH-1 Genel Maksat Helikopteri Operator Talimnamesi Tamamlayıcı Ders Notları. Kr.Hvcl. K.lıgı Matbaası,2009, 9-11,Ankara.

[12] T. Takagi and M. Sugeno, Fuzzy identi.cation of systems and its applications to modeling and control, IEEE Trans.Syst., Man, Cybern, 15:116.132, 1985.

[13] Zadeh , L., A., 1965. Fuzzy Sets .Inf Control, 8,338-353.

[14] Zadeh, L., A., 1978.Fuzzy Sets as a Basis for a Theory of Posibility.Fuzzy Sets Syst, 1, 3-28.

[15] Zadeh,L., The consept of a linguistic varia,ble and its application to approximate reasoning . I.Information Sciences,8(3), 199-249, (1975)

Ahmet Sahiner: Suleyman Demirel University, Faculty Art and Science of Science, Department of Mathematics, Isparta,Turkiye, [email protected]

Reyhane Ercan: Suleyman Demirel University, Faculty of Art and Science, Department of Mathematics, Isparta,Turkiye, [email protected]


173 Determination of Effects of Brassinosteroid Applicationson Secondary Metabolite Accumulation in Salt StressedPeppermint (Mentha piperita L.) by Modern OptimizationTecniquesAhmet Sahiner, Tuba Yigit, Ozkan Coban and Nilgun Gokturk

Baydar

Some classical methods remain incapable for the modeling of complex systems. Application of these methods can be costlyand time consuming to regulate tha data due to the excess of variable especially, in other disciplines such as medicine,agriculture, biology, econometrics. The fuzzy logic approach is a useful mathematical tool to eliminate these troubles. Byusing this method the new data is optained for untested conditions under the NaCl stress and comments In this study,the effect of different levels (0, 05, 1,5 and 2,5 mg/l) of 24 epibrassinolidone, an active form of brassinosteroid, on theaccumulation of essential oil yield and total phenolic content in peppermint (Mentha piperita L.) plants grown in the mediacontaining 0,100 and 150 mM NaCl was modelled by the fuzzy logic approach.

References[1] E.E. Aziz, H. Al-Amier, L.E. Craker, Influence of Salt Stress on Growth and Essential Oil Production in Peppermint,

Pennyroyal, and Apple Mint. Journal of Herbs, Spices and Medicinal Plants, (2008), 14 (1 - 2), 77-87.

[2] S. Khorasaninejad, A. Mousavi, H. Soltanloo, K. Hemmati, A. Khalighi, The Effect of Salinity Stress on GrowthParameters, Essential oil Yield and Constituent of Peppermint (Mentha piperita L.). World Applied Sciences Journal,11 (11), 1403-1407, (2010).

[3] S. Queslati, N. Karray-Bouraoui, H. Attia, M. Rabhi, R. Ksouri, M. Lachaal, Physiological and Antioxidant Responsesof Mentha pulegium (Pennyroyal) to Salt Stress. Acta Physiologiae Plantarum, (2010), 32(2), 289-96.

[4] V.L. Singleton, J.R. Rossi, Colorimetry of Total Phenolics with Phosphomolybdic-Phosphotungstic Acid, AmericanJournal of Enology and Viticulture, 16, 144-158, (1965).

[5] S.J. Tabatabaie, J. Nazari, Influence of Nutrient Concentration and NaCl Salinity on Growth, Photosynthesis andEssential Oil Content of Peppermint and Lemon verbena. Turkish Journal of Agriculture, (2007), 31, 245-53.

[6] L.A. Zadeh Fuzzy sets, Inform. Control,8, 338-353, (1965).

[7] M. Saltan, S. Saltan, A. Sahiner, Fuzzy logic modeling of deflection behavior aganist dynamic loading in flexible pave-ments, Construction and Building Materials, 21, 1406-1414 (2007).

[8] E. H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, International Journalof Man-Machine Studies 7 (1), 1-13 (1975).

[9] Sahiner, A., Gokkaya, H., Ucar, Nazım., Nonlinear Modelling of the Layer Microhardnes of Fe-Mn Binory Allays, Journalof Balkan Tribological Association, 4,508-519, (2013).

Ahmet Sahiner: Suleyman Demirel University, Department of Mathematics, Cunur, Isparta, Turkiye, [email protected]

Tuba Yigit: Suleyman Demirel University, Department of Mathematics, Cunur, Isparta, Turkiye, [email protected] Coban: Suleyman Demirel University, Department of Agricultural Biotechnology, Cunur, Isparta, Turkiye,

[email protected] G.Baydar: Suleyman Demirel University, Department of Agricultural Biotechnology, Cunur, Isparta, Turkiye,

[email protected]


174 On a Completeness Property of C(X) Equipped with a Set-Open TopologySmail Kelaiaia

Let C(X) be the set of all real-valued continuous functions on a topological space X. We give, in the framework of aparticular set-open topology defined on C(X) and by using a topological game, some conditions for C(X) to be weaklyα−favorable. favorable. This generalize some results obtained by R.A McCoy and I. Ntantu for the compact-open topology.

Department of Mathematics University of Annaba, Algeria, [email protected]


175 Existence of Solutions of a Class of Second Order Differ-ential InclusionsD.Azzam-Laouir and F.Aliouane

In the present paper we prove, in a separable Banach space, the existence of solutions for the second order sweeping processof the form

−..x ∈ NK(t)(.x(t)) + F (t, x(t),

.x(t)), a.e.t ∈ [0, T ],

where F is an upper semicontinuous set-valued mapping with nonempty closed convex values, K a nonempty ball compactand r−prox-regular E−set-valued mapping and NK(t)(.) the proximal normal cone of K(t).

References[1] F. Bernicot, J. Venel, Existence of sweeping process in Banach spaces under directional prox-regularity. J. Convex Anal.

17 (2010), 451-484.

[2] M. Bounkhel and L. Thibault, Nonconvex sweeping process and prox-regularity in Hilbert space. J. Nonlinear ConvexAnal. 6 (2001), 359-374.

[3] L. Thibault, Sweeping process with regular and nonregular sets. J. Diff. Equations 193 no. 1 (2003), 1-26.

Laboratory of Pure and Applied Mathematics, University of Jijel, Algeria, [email protected]


176 Applications of Generalized Fibonacci Autocorrelation Se-quences Γk,n (τ)∞τSibel Koparal and Nese Omur

In this study, we give the elements of the generalized Fibonacci Autocorrelation sequences

Γk,n (τ)∞τ

defined as

Γk,n (τ)def= Γn (Uki, τ) .

and some interesting sums involving the numbers Γk,n (τ) , where odd integer number k and nonnegative integers τ, n. Forexample, we show that

n∑τ=0

Γk,n (τ) =

[Uk(n+1) + Ukn − Uk

Vk

]2

,

Vk

n∑τ=0

(−1)τ Γk,n (τ) =

(Uk(n+1) − Ukn + Uk

)Vk

2

, if n is odd

Uk(n+1)Ukn, if n is even.

References[1] P. Filipponi and H. T. Freitag, Autocorrelation Sequences, The Fibonacci Quarterly, Vol.32, No.4, pp.356-368, 1994.

[2] T. Koshy, Fibonacci and Lucas Numbers with Applications. Pure and Applied Mathematics, Wiley-Interscience, NewYork, 2001.

[3] S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section. John Wiley & Sons, Inc., New York, 1989.

[4] E.Kılıc and P. Stanica, Factorizations and Representations of Second Order Linear Recurrences with Indices in Arith-metic Progressions, Bol. Soc. Mat. Mex. III. Ser., Vol.15, No.1, pp.23-35, 2009.

Sibel Koparal: Kocaeli University, Faculty of Arts and Sciences, Department of Mathematics, Izmit, Kocaeli-Turkiye,[email protected]

Nese Omur: Kocaeli Universitesi, Faculty of Arts and Sciences, Department of Mathematics, Izmit, Kocaeli-Turkiye,[email protected]


177 The Computer Simulation of Nuclear Magnetic ResonanceHyperfine Structure Constant for AB2, A2B2 and A2B3 Sys-tems Containing Some Organic Molecules with Spin 1

2 UsingJacobi ProgrammeHuseyin Ovalıoglu, Adnan Kılıc and Handan Engin Kırımlı

The energy matrices of molecules of AB2, A2B2 and A2B3 type have been calculated for three different chemical shiftsand several indirect spin-spin coupling coefficients (Jij) to obtain Nuclear Magnetic Resonance (NMR) hyperfine structureof such systems. The JACOBI programme were used to calculate eigenvalues and eigenvectors of these systems . Wehave developed a programme to calculate the transition probabilities and the transition energies. It is observed that thetheoretically calculated spectra is in agreement with the experimental spectra.

Keyword: Nuclear Magnetic Resonance (NMR)

References[1] A. Abragam, The Principles of Nuclear Magnetism, Oxford, (1973).

[2] J. W. Akitt, NMR and Chemistry, An Introduction to Modern NMR Spectroscopy, Chapman & Hall, London, (1992).

[3] F. Apaydın, Magnetik Rezonans, Temel Ilkeler, Deney Duzenekleri, Olcum Yontemleri, H.U. Muh. Fak. Ders Kit. No:3,Ankara, (1991),

[4] P. L. Corio, Structure of High-Resolution NMR Spectra., Academic Press New York, (1966), p202.

Huseyin Ovalıoglu: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]

Adnan Kılıc: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]

Handan Engin Kırımlı: Uludag University, Faculty of Science, DEpartment of Physics, Gorukle, Bursa-Turkiye, [email protected]

This work was supported by the Commission of Scientific Research Projects of Uludag University, Project numberOUAP(F)-2012/30.


178 The Computer Simulation of Nuclear Magnetic ResonanceHyperfine Structure Constant for ANX, ABC and A3BCSystems Containing Some Organic Molecules with Spin 1

2

Using Jacobi ProgrammeHuseyin Ovalıoglu, Handan E.Kırımlı, Cengiz Akay and Adnan

Kılıc

The energy matrices of molecules of ANX, ABC and A3BC type have been calculated values of four different chemical shiftsand several indirect spin-spin coupling coefficients (Jij) to obtain Nuclear Magnetic Resonance (NMR) hyperfine structureof such systems. The JACOBI programme were used to calculate eigenvalues and eigenvectors of these systems . We havedeveloped a programme to calculate the transition probabilities and the transition energies. Also, it has been observed thatthe theoretically calculated spectra is in agreement with the experimental spectra for molecule of ANX.

Keyword: Nuclear Magnetic Resonance (NMR)

References[1] A. Abragam, The Principles of Nuclear Magnetism, Oxford, (1973).

[2] J. W. Akitt, NMR and Chemistry, An Introduction to Modern NMR Spectroscopy, Chapman & Hall, London, (1992).

[3] F. Apaydın, Magnetik Rezonans, Temel Ilkeler, Deney Duzenekleri, Olcum Yontemleri, H.U. Muh. Fak. Ders Kit. No:3,Ankara, (1991),

[4] D. W. Mathieson, NMR For Organic Chemists, Academic Press, London, (1967),

[5] P. L. Corio, Structure of High-Resolution NMR Spectra, Academic Press, New York, (1966).

Huseyin Ovalıoglu: Uludag University, Faculty of Science, DEpartment of Physics, Gorukle, Bursa-Turkiye, [email protected]

Handan Engin Kırımlı: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]

Cengiz Akay: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]

Adnan Kılıc: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]



179 Necessary and Sufficient Conditions for First Order Differ-ential Operators to be Associated with a Disturbed DiracOperator in Quaternionic AnalysisUgur Yuksel

Recently the initial value problem

∂tu = Lu :=

3∑i=1

A(i)(t, x)∂xiu+B(t, x)u+ C(t, x)

u (0, x) = u0(x)

has been solved uniquely by N. Q. Hung [1] using the method of associated spaces constructed by W. Tutschke [2] in thespace of generalized regular functions in the sense of quaternionic analysis satisfying the equation

Dαu := Du+ αu = 0, α ∈ R

where D =3∑j=1

ej∂xj is the Dirac operator, and t is the time variable. Only sufficient conditions has been obtained in [1]

for the operators L and Dα to be associated.In the present talk we will prove necessary and sufficient conditions for the underlined operators to be associated. This

criterion makes it possible to construct all linear operators L for which the initial value problem with an arbitrary initialgeneralized regular function is always solvable. Further we will correct a mistake made in the calculation of the interiorestimate in [1].

References[1] N. Q. Hung, Initial Value Problems in Quaternionic Analysis with a Disturbed Dirac Operator, Adv. appl.

Clifford alg., Vol. 22, Issue 4 (2012), pp. 1061-1068.

[2] W. Tutschke, Solution of initial value problems in classes of generalized analytic functions, Teubner Leipzigand Springer Verlag, 1989.

Atilim University, Ankara, Turkey, [email protected]


180 Theoretical Investigation of Substituent Effect on the Car-bonyl Stretching VibrationIlhan Kucuk and Aslı Ayten Kaya

Gaussian 03 is the electronic structure program, is used by chemists, chemical engineers, biochemists, physicists and othersfor research in established and emerging areas of chemical interest. Starting from the basic laws of quantum mechanics,Gaussian predicts the energies, molecular structures, and vibrational frequencies of molecular systems, along with numerousmolecular properties derived from these basic computation types. In this study, the molecular geometry and vibrationalfrequencies of substitute isonitrosoacetophenone (inapH) molecules in the ground state have been calculated using densityfunctional method (B3LYP) with the 6− 311 + +G(d, p) basis set. The values calculated by the Gaussian 03 program wereused to the artificial neural network. The developed neural network, which has four input neurons, one output neuron,four hidden layers, five, six, seven and eight neurons of hidden layers and full connectivity between neurons. The inputparameters were electronegativity, dipole moment, C and O Mulliken charges. A total of 240 input vectors obtained fromvaried samples were available in the training data. The results show that the ANN model has a 99% correlation withGaussian program data. All statistical values prove that the proposed ANN model is suitable to predict the vibrationfrequency values very close to the results of the calculated values.

Ilhan Kucuk: Uludag University, Faculty of Science, Department of Chemistry, Gorukle, Bursa-Turkiye, [email protected]

Aslı Ayten Kaya: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]


181 Modeling of the Optical Properties of the CdS Thin Filmsby Using Artificial Neural NetworkAslı Ayten Kaya, Kadir Erturk, Nil Kucuk and Ilker Kucuk

In this study, CdS thin films were produced by electro-deposition method. Optical properties of thin films were investigatedUV-Vis. Spectrophotometer. A new model was developed with experimental data using by Artificial Neural Network (ANN).This model has three hidden layers with twenty-one neurons and full connectivity between them. The input parameterswere sample number (n), absorbance (A), thickness (d) and absorbance constant (α). A total of 2400 input vectors wereavailable in the training and testing data. The number of hidden layers and neurons in each layer were determined throughtrial and error to be optimal including different transfer functions such as hyperbolic tangent, sigmoid and hybrid. Afterthe network was trained, a better result was obtained from the network formed by the hyperbolic tangent transfer functionin the hidden and output layers. The number of epochs was 106 for training.

Aslı Ayten Kaya: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]

Kadir Erturk: Namik Kemal University, Faculty of Science, Department of Physics, Merkez, Tekirdag-Turkiye, [email protected]

Nil Kucuk: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye,[email protected]

Ilker Kucuk: Uludag University, Faculty of Science, Department of Physics, Gorukle, Bursa-Turkiye, [email protected]



182 Nonprinciple Solutions and Extensions of Wong’s Oscilla-tion Criteria to Forced Second-Order Impulsive and DelayDifferential EquationsAbdullah Ozbekler and Agacık Zafer

Wong’s well-known oscillation theorem states that if z is a positive nonprincipal solution of

(r(t)x′)′ + q(t)x = 0, t ≥ a

satisfyinglimt→∞

H(t) = − limt→∞

H(t) =∞,

where

H(t) :=

∫ t

a

1

r(s)z2(s)

(∫ s

az(σ)f(σ)dσ

)ds,

then every solution of(r(t)x′)′ + q(t)x = f(t)

is oscillatory.In this talk, we give some extentions of above result to impulsive and delay differential equations. It is shown that the

oscillation behavior may be altered due to presence of the delay and impulse action. Extensions to Emden-Fowler typeimpulsive and delay equations are also provided.

References[1] M. Morse and W. Leighton, Singular quadratic functionals, Trans. Amer. Math. Soc. 40, 252–286, (1936).

[2] James S.W. Wong, Oscillation criteria for forced second-order linear differential equation, J. Math. Anal. Appl.231, 235–240 (1999).

[3] A. Ozbekler, James S.W. Wong and A. Zafer, Forced oscillation of second-order nonlinear differential equationswith positive and negative coefficients, Appl. Math. Lett. 24, 1225–1230 (2011).

Atilim University, Ankara, Turkey, [email protected]


183 Modeling of Exposure Buildup Factors for Concrete Shield-ing Materials up to 10 mfp Using Generalized Feed-ForwardNeural NetworkNil Kucuk, Vishwanath P.Singh and N.M.Badiger

In this work, generalized feed-forward neural network (GFFNN) was presented for the computation of the gamma-rayexposure buildup factors (BD) of the seven concrete shielding materials [ordinary (OR), hematite-serpentine (HS), ilmenite-limonite (IL), basalt-magnetite (BM), ilmenite ((IT), steel-scrap (SS), steel-magnetite (SM)] in the energy region 0.03-15MeV, and for penetration depths up to 10 mean free path (mfp). The GFFNN has been trained by a Levenberg-Marquardt learning algorithm. The developed model is in 99% agreement with the ANSI/ANS-6.4.3 standard data set.Furthermore, the model is fast and does not require tremendous computational efforts. The estimated BD data for concreteshielding materials have been given with penetration depth and incident photon energy as comparative to the results of theinterpolation method using the Geometrical Progression (G-P) fitting formula.

Nil Kucuk: Uludag University, Faculty of Art and Sciences, Department of Physics, Gorukle Campus, 16059 Bursa,Turkey, [email protected]

Vishwanath P.Singh: Karnatak University, Department of Physics, Dharwad, 580003, India and Health Physics Section,Kaiga Atomic Power Station-3&4, NPCIL, Karwar 581400, India, [email protected]

N.M.Badiger: Karnatak University, Department of Physics, Dharwad, 580003, India, [email protected]


184 Calculation of Gamma-Ray Exposure Buildup Factors forSome Biological SamplesNil Kucuk, Vishwanath P.Singh and N.M.Badiger

Gamma-ray exposure buildup factors (EBF) have been calculated for some biological samples (viz. lungs, pancreas, andovaries) in the energy region 0.015–15 MeV, up to penetration depths of 40 mean free paths (mfp). The five-parametergeometric progression (G-P) fitting approximation and ANSI/ANS-6.4.3-1991 (American National Standard) library havebeen used to calculate EBF. The EBF have been studied as functions of incident photon energy and penetration depth.The variations in the EBF, for all the biological samples, in different energy regions, have been presented in the form ofgraphs. Buildup factors of these biological samples cannot be found in any standard database, so these studies will help inestimating safe dose levels for radiotherapy patients.


Vishwanath P.Singh: Karnatak University, Department of Physics, Dharwad, 580003, India and Health Physics Section,Kaiga Atomic Power Station-3&4, NPCIL, Karwar 581400, India, [email protected]

N.M.Badiger: Karnatak University, Department of Physics, Dharwad, 580003, India, [email protected]


185 Determination of Thermoluminescence Kinetic Parametersof ZnB2O4: La PhosphorsNil Kucuk, A.Halit Gozel, Mustafa Topaksu and Mehmet Yuk-

sel

Thermoluminescence (TL) glow curves of 1%, 2%, 3% and 4% ZnB2O4: La phosphors synthesized by nitric acid methodwere obtained by irradiation at the dose range of 143 mGy - 60 Gy with 90Sr/90Y beta source, which has 40 mCi activity,included in the Risø TL/OSL DA-20 reader system. TL glow curves were recorded after pre-heating process at 140 C andthen heating up to 450 C in nitrogen atmosphere at a constant heating rate of 5 C/s. In this study, with the help ofglow curve readings, kinetic parameters of the main TL glow peaks of ZnB2O4: La phosphors (i.e. activation energies andfrequency factors) were determined and evaluated by the method of Computerized Glow Curve Deconvolution (CGCD),Peak Shape (PS) method and Initial Rise (IR) method. In conclusion, kinetic parameters found in this study by themethods applied to ZnB2O4: La phosphors were consistent with each other.


Aziz Halit Gozel: Adiyaman University, Faculty of Art and Sciences, Department of Physics, 02040 Adiyaman, Turkey,[email protected]

Mustafa Topaksu: Cukurova University, Faculty of Art and Sciences, Department of Physics, 01330 Adana, Turkey,[email protected]

Mehmet Yuksel: Cukurova University, Faculty of Art and Sciences, Department of Physics, 01330 Adana, Turkey,[email protected], [email protected]


186 Improved Numerical Radius and Spectral Radius Inequal-ities for OperatorsFuad Kittaneh and Amer Abu-Omar

We establish an improvement of the triangle inequality for the numerical radius and give necessary and sufficient condi-tions for the equality case. New numerical radius and spectral radius inequalities are also given. Our results include animprovement of a well-known spectral radius inequality concerning the subadditivity property for commuting operators.

Department of Mathematics, The University of Jordan, Amman, Jordan and Al-Ahliyya Amman University, Deanshipof Graduate Studies and Scientific Research, Amman, Jordan, [email protected]


187 n-Dimensional Sobolev type spaces involving Chebli-TrimecheTransformMourad Jelassi

Using Chebli Trimeche transform, we define and study n-Dimensional Sobolev type spaces. In particular, we give someproperties including completeness and boundedness of convolution product in these spaces. Next, a Titchmarch type theoremfor the Chebli Trimeche transform is investigate.

Carthage University, ISSAT Mateur, Department of Mathematics, 7030 Mateur-Bizerte, Tunisia,[email protected]


188 A Fixed Point Theorem for Multivalued Mappings withδ-Distance on Complete Metric SpaceOzlem Acar and Ishak Altun

In this talk, we mainly study on fixed point theorem for multivalued mappings with δ-distance using Wardowski’s techniqueon complete metric space. Let (X, d) be a metric space and B(X) be family of all nonempty bounded subsets of X. Defineδ : B(X)×B(X)→ R by

δ(A,B) = sup d(a, b) : a ∈ A, b ∈ B .Considering δ-distance, it is proved that if (X, d) be a complete metric space and T : X → B(X) be a multivalued certaincontraction, then T has a fixed point.

References[1] Fisher, B., Common fixed points of mappings and set-valued mappings. Rostock. Math. Kolloq. No. 18 (1981), 69–77.

[2] Fisher, B., Fixed points for set-valued mappings on metric spaces. Bull. Malaysian Math. Soc. (2) 4 (1981), no. 2, 95–99.

[3] Fisher, B., Set-valued mappings on metric spaces. Fund. Math. 112 (1981), no. 2, 141–145.

[4] Fisher, B., Common fixed points of set-valued mappings. Punjab Univ. J. Math. (Lahore) 14/15 (1981/82), 155–163.

[5] Hicks, T. L., Fixed point theorems for multivalued mappings. Indian J. Pure Appl. Math. 20 (1989), no. 11, 1077–1079.

[6] Hicks, T. L., Set-valued mappings on metric spaces. Indian J. Pure Appl. Math. 22 (1991), no. 4, 269–271.

[7] Altun, I., Fixed point theorems for generalized ϕ-weak contractive multivalued maps on metric and ordered metricspaces. Arab. J. Sci. Eng. 36 (2011), no. 8, 1471–1483.

[8] Mınak, G.; Acar, O.; Altun, I., Multivalued pseudo-Picard operators and fixed point results. J. Funct. Spaces Appl.2013, Art. ID 827458, 7 pp.

Ozlem Acar: Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahsihan, 71450, Kirikkale-Turkey, [email protected]

Ishak Altun: Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahsihan, 71450, Kirikkale-Turkey, [email protected]


189 Existence of Solutions of α ∈ (2, 3] Order Fractional ThreePoint Boundary Value Problems with Integral ConditionsSinem Unul and N.I.Mahmudov

In this talk, existence of solutions for α ∈ (2, 3] order fractional differential equations with three point fractional boundaryand integral conditions will be discussed:

Dα0+u(t) = f

(t, u(t),Dβ1

0+u(t),Dβ20+u(t)

); 0 ≤ t ≤ T ; 2 < α ≤ 3

with the two point and integral boundary conditions

a0u(0) + b0u(T ) = λ0

T∫0

g0(s, u (s))ds,

a1Dβ10+u(η) + b1D

β10+u(T ) = λ1

T∫0

g1(s, u (s))ds, 0 < β1 ≤ 1, 0 < η < T,

a2Dβ20+u(η) + b2D

β20+u(T ) = λ2

T∫0

g2(s, u (s))ds, 1 < β2 ≤ 2,

where Dα0+ denotes the Caputo fractional derivative of order α.

References[1] Agarwal, RP, Benchohra, M, Hamani, S: A survey on existence results for boundary value problems of nonlinear fractional

differential equations and inclusions. Acta Appl. Math. 109, 973-1033 (2010)

[2] Bai, ZB: On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Anal. 72, 916-924 (2010)

[3] Ahmad, B, Nieto, JJ, Alsaedi, A: Existence and uniqueness of solutions for nonlinear fractional differential equationswith non-separated type integral boundary conditions. Acta Math. Sci. 31, 2122-2130 (2011)

[4] Ahmad, B, Ntouyas, SK: Nonlinear fractional differential equations and inclusions of arbitrary order and multi-stripboundary conditions. Electron. J. Differ. Equ. 2012, Article ID 98 (2012)

[5] Bai, ZB, Sun, W: Existence and multiplicity of positive solutions for singular fractional boundary value problems.Comput. Math. Appl. 63, 1369-1381 (2012)

[6] Ahmad, B, Ntouyas, SK: A boundary value problem of fractional differential equations with anti-periodic type integralboundary conditions. J. Comput. Anal. Appl. 15, 1372-1380 (2013) 23.

[7] Ahmad B. , Ntouyas S. K and Alsaedi A., On fractional differential inclusions with anti-periodic type integral boundaryconditions, Boundary Value Problems 2013, 2013:82.

[8] M. Aitaliobrahim, “Neumann boundary-value problems for differential inclusions in banach spaces,” Electronic Journalof Differential Equations, vol. 2010, no. 104, pp. 1–5, 2010.

Sinem Unul: Eastern Mediterranean University, Department of Mathematics, Gazimagusa, TRNC, Mersin 10, Turkey,[email protected]

N.I.Mahmudov: Eastern Mediterranean University, Department of Mathematics, Gazimagusa, TRNC, Mersin 10,Turkey, nazim. [email protected]


190 Vector-Valued Variable Exponent Amalgam SpacesIsmail Aydın

In this talk, we define the vector-valued (Banach space valued) variable exponent amalgam spaces and discuss the basicproperties, the dual space, the reflexivity and some embedding properties of these spaces.

References[1] I. Aydın and A.T. Gurkanlı, Weighted Variable Exponent Amalgam spaces W (Lp(x), Lqw), Glasnik Matematicki, Vol.

47(67), (2012), 165-174.

[2] I. Aydın, On Variable Exponent Amalgam Spaces, Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matem-atica, Vol. 20(3),(2012), 5-20.

[3] A. T. Gurkanlı and I. Aydın, On The Weighted Variable Exponent Amalgam Space W (Lp(x), Lqw), Acta MathematicaScientia, 34B(4),(2014), 1–13.

[4] V. Kokilashvili, A. Meskhi and M. A. Zaighum, Weighted Kernel Operators in Variable Exponent Amalgam Spaces,Journal of Inequalities and Applications, (2013), 2013:173.

[5] A. T. Gurkanlı, The Amalgam Space W (Lp(x), Lpn) and Boundedness of Hardy-Littlewood Maximal Operators,ISAAC 2013 Proceeding (Accepted for publication).

[6] A. Meskhi and M. A. Zaighum, On The Boundedness Of Maximal And Potential Operators In Variable ExponentAmalgam Spaces, Journal of Mathematical Inequalities, Volume 8(1), (2014), 123–152.

[7] C. Cheng and J. Xu, Geometric Properties of banach Space Valued Bochner-Lebesgue Spaces With Variable Exponent,Journal of Mathematical Inequalities, Vol. 7(3), (2013), 461-475.

[8] D. V. Lakshmi and S. K. Ray, Vector-valued Amalgam Spaces, International Journal of Computational Cognition(http://www.ijcc.us), VOL. 7(4), (2009), 33-36.

[9] D. V. Lakshmi and S. K. Ray, Convolution Product on Vector-valued Amalgam Spaces, International Journal of Com-putational Cognition (http://www.ijcc.us), VOL. 8(3), (2010), 67-73.

Sinop University, Faculty of Science and Letters, Department of Mathematics, Sinop-Turkiye, [email protected]


191 Soliton Solutions of Sawada–Kotera Equation by HirotaMethodEsra Karatas and Mustafa Inc

In this work the Sawada–Kotera equation is studied. The Hirota Bilinear Method is used to determine multiple-solitonsolutions for this equation. By means of this method, three soliton solutions for fifth order nonlinear partial differentialequation is formally obtained.

Esra Karatas: Canakkale Onsekiz Mart University, Gelibolu Piri Reis Vocational School, Department of, Mathematics,Canakkale-Turkiye, [email protected]

Mustafa Inc: Firat University, Science Education, Department of Mathematics, Elazg-Turkiye, [email protected] work was supported by Canakkale Onsekiz Mart University


192 Certain Quasi-Cyclic Codes which are Hadamard CodesMustafa Ozkan and Figen Oke

A n × n matrix such that all components are −1 or 1 and M.Mt = n.I is called Hadamard matrix. A code obtained byusing a Hadamard matrix is called Hadamard code. In this study it is shown that Hadamard codes which have codewordsin the ring F2 + vF2 can be obtained by some special matrices lexicographically ordered. This relation is obtained by usingtwo different Gray maps from (F2 + vF2)n to F 2n

2 .

References[1] Krotov, D. S. Z4-linear perfect codes ,Diskretn. Anal. Issled. Oper. Ser.1.Vol.7, 4,2000 P. 78-90.

[2] Krotov,D. S. Z4-linear Hadamard and extended perfect codes, Procs. of the International Workshop on Coding andCryptography,Paris, 2001, pp. 329-334.

[3] Jian-Fa,Q. , Zhang L.N. and Zhu S.X.,(1 + u)- cyclic and cyclic codes over the ring F2 + uF2 ,Applied MathematicsLetters,19,2006,820-823.

[4] Jian-Fa Qian, Li-Na Zhang and Shi-Xin Zhu, Constacyclic and cyclic codes over F2 + uF2 + u2F2, IEICE Trans.Fundamentals, E89-A, No 6, 2006,1863-1865.

[5] Vermani, L. R., Elements of Algebraic Coding Theory, Chapman Hall , India., 1996.

Mustafa Ozkan: Trakya University, Faculty of Science, Department of Mathematics, Edirne-Turkiye, [email protected]

Figen Oke: Trakya University, Faculty of Science, Department of Mathematics, Edirne-Turkiye, [email protected]


193 Pointwise Convergence of Derivatives of New Baskakov-Durrmeyer-Kantorovich Type OperatorsGulsum Ulusoy, Ali Aral and Emre Deniz

Recently in [1], we have constructed a new sequence of integral type operators which contain characteristic properties ofBaskakov Durrmeyer and Baskakov Kantorovich opearators. In this talk, we continue focus on pointwise convergence ofderivatives of these operators by the means of Voronoskaya type asymptotic formula. Moreover, to describe the rate ofconvergence and an estimate of error in terms of modulus of continuity in simultaneous approximation (approximation ofderivatives of functions by the corresponding order derivatives of operators) by this new durrmeyer operators, we presentVoronovskaya type asymtotic formula in quantitative form.

References[1] Deniz, E., Aral, A. and Ulusoy, G., New Integral Type Operators, (submitted)

[2] Deo, N., Direct result on exponential-type operators, Appl. Math. Comput., 204 (2008), 109n115.

[3] Gadjiev, A.D., Ibragimov, I.I., On a sequence of linear positive operators, Soviet Math. Dokl., 11 (1970), 1092-1095.

[4] Kasana, H.S., Agrawal, P.N., Gupta, Vijay: Inverse and saturation theorems for linear combination of modifed Baskakovoperators, Approx. Theory Appl., 7(2) (1991), 65-82.

[5] Stan, I. G., On the Durrmeyer-Kantorovich type operator, Bulletin of the Transilvania University of Brasov, Vol 6 (55),No. 2, 2013.

Gulsum Ulusoy: Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahsihan, 71450,Kirikkale-Turkey, [email protected]

Ali Aral: Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahsihan, 71450, Kirikkale-Turkey, [email protected]

Emre Deniz: Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahsihan, 71450, Kirikkale-Turkey, [email protected]


194 On the High Order Lipschitz Stability of Inverse NodalProblem for String EquationEmrah Yılmaz and Hikmet Koyunbakan

Inverse nodal problem on the string operator is the finding the density function using nodal sequence z(n)k . In this paper,

we solve a stability problem using nodal set of eigenfunctions and show that the space of high order density functions ishomeomorphic to the partition set of the space of quasinodal sequences. Basically, this method is similar to [1] and [2]which is given for Sturm-Liouville and Hill operators, respectively.

References[1] C. K. Law and J. Tsay, On the well-posedness of the inverse nodal problem, Inverse Problems, 2001, 17: 1493-1512.

[2] Y. H. Cheng and C. K. Law, The inverse nodal problem for Hill’s equation, Inverse Problems, 2006, 22: 891-901.

[3] V. A. Ambartsumyan, Uber eine frage der eigenwerttheorie, Zeitschrift fur Physik, 1929, 53: 690-695.

[4] B. M. Levitan and I. S. Sargsjan, Introduction to spectral theory: Self adjoint ordinary differential operators, AmericanMathematical Society, Providence, Rhode Island, 1975.

[5] J. R. McLaughlin, Analytic methods for recovering coefficients in differential equations from spectral data, SIAM, 1986,28: 53-72.

[6] J. Poschel and E. Trubowitz, Inverse spectral theory, volume 130 of Pure and Applied Mathematics, Academic Press,Inc, Boston, MA, 1987.

[7] C. F. Yang and A. Zettl, Half inverse problems for quadratic pencils of Sturm-Liouville operators, Taiwanese Journalof Mathematics, 2012, 16(5): 1829-1846.

Emrah Yılmaz: Department of Mathematics, Firat University, Elazıg-Turkiye, [email protected] Koyunbakan: Department of Mathematics, Firat University, Elazıg-Turkiye, [email protected]


195 Positive Solutions of a Boundary Value Problem with Deriva-tives in the Nonlinear TermPatricia J.Y.Wong

We consider the Sturm-Liouville boundary value problemy(m)(t) + F

(t, y(t), y′(t), · · · , y(q)(t)

)= 0, t ∈ [0, 1]

y(k)(0) = 0, 0 ≤ k ≤ m− 3

ζy(m−2)(0)− θy(m−1)(0) = 0, ρy(m−2)(1) + δy(m−1)(1) = 0

where m ≥ 3, 1 ≤ q ≤ m− 2, λ > 0 and F is continuous at least in the domain of interest. It is noted that boundary valueproblems with derivative-dependent nonlinear terms are seldom investigated in the literature due to technical difficulty. Inthis talk, we employ a new technique to establish existence of positive solutions of the boundary value problem.

Nanyang Technological University, School of Electrical and Electronic Engineering, 50 Nanyang Avenue, Singapore639798, Singapore, [email protected]


196 One Step Iteration Scheme for Two Multivalued Mappingsin CAT(0) SpacesIzhar Uddin and M.Imdad

In this paper, we study the one step iteration scheme for two multivalued nonexpansive mappigs in CAT(0) spaces andprove ∆−convergence as well as strong convergence theorems. Thus, our results generalize and extend many relevant resultsin Abbas et al. (Appl. Math. Lett. 24 (2011), no. 2, 97-102), Khan (Bull. Belg. Math. Soc. Simon Stevin 17 (2010)127-140), Khan (Nonlinear Anal. 8 (2005) 1295-1301) and Fukhar-ud-din (J. Math. Anal. Appl. 328 (2007) 821-829) andreferences cite therein.

Department of Mathematics, Aligarh Muslim University, Aligarh-202002, Uttar Pradesh, India, [email protected], [email protected]


197 A Variant Akaike Information Criterion for Mixture Au-toregressive Model SelectionFaycal Hamdi

In this talk, we consider the problem of order selection of Mixture Autoregressive (MAR) models. These models are amongthe most powerful tools for modelling some stylized features exhibited by many time series such as multimodality, tailheaviness, change in regime and asymmetry. We aim to present a variant of the Akaike information criterion (AIC), forMAR model selection, based on complete-data rather than incomplete-data and which different from the standard criteria.We compare the performance of our proposed criterion to that of the traditional AIC criterion and certain other competitorsin a simulation study.

References[1] Akaike, H. (1973). Infonuation theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki,

F. (Eds.), Proe. 2nd Internat. Syrup. on Inform. Theory. Akademia Kiado, Budapest, 267-281.

[2] Cavanaugh, J. E. and Shumway, R. H. (1998). An Akaike information criterion for model selection in the presence ofincomplete data. J. Stat. Plan. Infer., 67, 45-65.

[3] Dempster, A.P., Laird, N.M., Rubin and D.B., (1977). Maximum likelihood from incomplete data via the EM algorithm(with discussion). J.Roy. Statist. Soc. B 39, 1–38.

[4] Wong, C. and Li,W., (2000). On a mixture autoregressive model. J. Roy. Statist. Soc. Ser. B, 62, 95-115.

RECITS Laboratory, Faculty of Mathematics, University of Science and Technology Houari Boumediene (USTHB), PoBox 32. El Alia, 16111, Bab Ezzouar, Algiers, Algeria, [email protected] or hamdi [email protected]


198 Zagreb Polynomials of Three graph OperatorsA.R.Bindusree, V.Lokesha, I.Naci Cangul and P.S.Ranjini

A topological index is a graph invariant applicable in chemistry.The first and second Zagreb indices are amongst theoldest and best known topological indices defined in 1972 by Gutman and are given different names in the literature, suchas the Zagreb group indices, the Zagreb group parameters and most often, the Zagreb indices. Zagreb indices were amongthe first indices introduced,and has been used to study molecular complexity, chirality,ZE-isomerism and hetero-systems.Zagreb indices exhibited a potential applicability for deriving multi-linear regression models. Let G be a connected graphwith n vertices and m edges.The vertex set and edge set are denoted by V (G) and E(G) respectively.For every vertex vi εV (G),where i = 1, 2, ...n, the edge connecting vi and vj is denoted by (vi, vj) and d(vi) denotes the degree of vertex vi inG. The first and the second zagreb indices are defined as follows.

M1(G) =∑

viεV (G)

[d(vi)2]

M2(G) =∑

(vi,vj)εE(G)

[d(vi).d(vj)].

First and Second zagreb polynomials are derived from First and Second Zagreb indices respectively. They are defined asfollows.

M1(G, x) =∑

vi,vjεE(G)

xd(vi)+d(vj)

M2(G, x) =∑

vi,vjεE(G)

xd(vi).d(vj)

where x is a dummy variable. Moreover, the First and Second zagreb indices can be obtained from its polynomial.Becausefor i = 1, 2

Mi(G) =∂Mi(G, x)

∂xThe third Zagreb index, M3(G) and third zagreb polynomial M3(G, x)are deined respectively as,

M3(G) =∑

(vi,vj)εE(G)

[|d(vi)− d(vj)|].

M3(G, x) =∑

(vi,vj)εE(G)

x|d(vi)−d(vj)|.

In this paper,the relation between Zagreb polynomials on three graph operators is discussed.we investigates the relationbetween Zagreb polynomial of a graph G and a graph obtained by applying the operators S(G),R(G) and Q(G).Moreover,relation between Zagreb polynomial of a graph G and its corona is also described.

References[1] Asadpour,Jafar.”Some Topological Indices of nanostructures”, Optoelectronics And Advanced Materials- Rapid Com-

munications, 5(2011):769-772.

[2] Astaneh-Asl, A., and Gholam Hossein Fath-Tabar. ”Computing the first and third Zagreb polynomials of Cartesianproduct of graphs.” Iranian J. Math. Chem 2.2 (2011): 73-78.

[3] Farahani,Mohammed Reza.”First and second Zagreb Polynomials of V C5C7[p, q] and HC5C7[p, q] nanotubes”,Int.Letters of Chemistry,Physics and Astronomy,12(2014):56-62.

[4] Farahani,Mohammed Reza.”Zagreb index, Zagreb Polynomial of Circumcoronene Series of Benezoid”. Advances inmaterials and Corrosion 2.1(2013):16-19.

[5] Farahani,Mohammed Reza.”Zagreb indices and Zagreb Polynomials of Polycyclic Aromatic HydrocarbonsPAHs”.Journal of chemica Acta 2.2(2013):70-72.

[6] Fath-Tabar, Gholam hossein. ”Zagreb Polynomial And Pi Indices Of Some Nano Structures.” Digest Journal of Nano-materials and Biostructures (DJNB) 4.1 (2009).

A.R.Bindusree: Sree Narayana Gurukulam College of EngineeringV.Lokesha: Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Bellary, India, v.lokesha

@gmail.com

Ismail Naci Cangul: Uludag University, Faculty of Science, Department of Mathematics, Bursa-Turkiye, [email protected]

Ranjini P.S: Department of Mathematics, Don Bosco Institute Of Technology,Bangalore-74, India, ranjini p [email protected]


199 A Note on the Moment Estimate for Stochastic FunctionalDifferential EquationsYoung-Ho Kim

In this talk, we are consider a stochastic functional differential equation with initial value under non-Lipschitz condition anda weakened linear growth condition. By applying the Ito formula, a class of moment estimates of the solution of stochasticdifferential equations is studied.

References[1] Y. El. Boukfaoui, M. Erraoui, Remarks on the existence and approximation for semilinear stochastic differential in

Hilbert spaces, Stochastic Anal. Appl. 20 (2002), 495-518.

[2] Y.J. Cho, S.S. Dragomir, Y-H. Kim: A note on the existence and uniqueness of the solutions to SFDEs. J. Inequal.Appl. 2012:126 (2012), pp. 1–16.

[3] T.E. Govindan, Stability of mild solution of stochastic evolution equations with variable delay, Stochastic Anal. Appl.21 (2003), 1059-1077.

[4] D. Henderson and P. Plaschko, Stochastic Differential Equations in Science and Engineering, World Scientific Pub-lishing Co. 2006.

[5] K. Liu, Lyapunov functionals and asymptotic of stochastic delay evolution equations, Stochastics and Stochastic Rep.63 (1998) 1-26.

[6] X. Mao, Stochastic Differential Equations and Applications, Horwood Publication Chichester, UK, 2007.

[7] X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, London, UK: Imperial CollegePress, 2006.

[8] Y. Ren and N. Xia, Existence, uniqueness and stability of the solutions to neutral stochastic functional differentialequations with infinite delay, Appl. Math. Comput. 210 (2009) 72-79.

[9] Y. Ren and N. Xia, A note on the existence and uniqueness of the solution to neutral stochastic functional differentialequations with infinite delay, Appl. Math. Comput. 214 (2009) 457-461.

[10] T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differential Equations 96(1992), 152-169.

[11] F. Wei and K. Wang, The existence and uniqueness of the solution for stochastic functional differential equations withinfinite delay, J. Math. Anal. Appl. 331 (2007), 516-531.

[12] Y. -H. Kim, An estimate on the solutions for stochastic functional differential equations , J. Appl. Math. and Infor-matics, 29 (2011) no.5-5, pp. 1549-1556.

[13] Y. -H. Kim, A note on the solutions of neutral SFDEs with infinite delay, J. Ineq. Appl., 2013 (2013) no.181,doi.10.1186/1029-142X-2013-181

Department of Mathematics Changwon National University, Changwon, 641-773, Korea [email protected]


200 Issues Optimization of Public AdministrationCanybec Sulayman and Gulnar Suleymanova

In this talk, we discuss optimization of computational aspects in public administration with example of Kyrgyzstan. Ourwork analyzes the inefficiencies in public administration in Kyrgyzstan and uses mathematical models to provide, in ouropinion, decision-making insight on how to reduce or completely eliminate effect of these inefficiencies. We will concludewith common challenges encountered by our researchers in application of these mathematical techniques.

References[1] Public Foundation Media Consulting Foundation, Analytical report on the research results of the level of access to

information and discussion of problems on the possible solutions in local communities. This research produced withsupport of the German Federal Ministry of Economic Cooperation and Development. (2014)

[2] European Bank for Reconstruction and Development, TRANSITION REPORT (2013)

[3] Kydyraliev S., Sulayman C., Suleymanova G., New taxation policy in Kyrgyzstan:Theory and practice. The 18thNISPAcee Annual Conference. Public Administration in Times of Crisis. Warsaw,Poland.

[4] Scott, Foresman, Functions, Statistics, and Trigonometry, The University of Chicago School Mathematics Project,Teacher’s Edition (1992) p.19.

[5] David M Diaz, Christopher D Barr, Mine Cetinkaya-Rundel, OpenIntro Statistics, Second Edition (2013)

Canybec Sulayman: University of California – Los Angeles (UCLA), Anderson School of Management, Candidate ofMasters in Business Administration, Los Angeles, CA, USA, [email protected]

Gulnar Suleymanova: Kyrgyzstan-Turkey Manas University, Institute of Natural and Applied Sciences, Candidate ofMaster’s Program in Mathematics, Bishkek–Kyrgyzstan, gulnara [email protected]

This work was not supported by any grant or university program.


201 Jacobi Orthogonal Approximation with Negative Integerand its ApplicationZhang Xiao-yong and Wan Zheng-su

In this paper, the Jacobi spectral method for ordinary differential equation is proposed, which is based on the Jacobiapproximation with negative integer. This method is very efficient for the initial value problem of the ordinary differentialequations. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracyof this new approach and coincide well with theoretical analysis.

References

[1] A.M.Stuart and A.R.Humphries,Dynamical systems and Numerical Analysis, Cambridge University Press, Cam-bridge,1996. 25.

[2] Ben-yu Guo, Jacobi Approximation in Certain Hilbert Spaces and Their Applications to Singualr Differential Equations,J.Math.Anal.Appl. (2000),373-408.

[3] Chao Zhang, Ben-Yu Guo and Tao Sun, Laguerre Spectral Method for High Order Problems,Numer.Math.Theor.Meth.Appl.Vol.6, No.3, pp.520-537(2013).

[4] D. J. Higham, Analysis of the Enright-Kamel partitioning method for stiff ordinary differential equations,IMAJ.Numer.Anal.,9(1989),1-14. 19.

[5] E. Hairer, C.Lubich, and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for OrdinaryDiffrential Equations,Springer Series in Comput.Mathmatics, Vol.31, Springer-Verlag, Berlin, 2002. 16.

[6] E.Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equation :Nonstiff Problems, Springer-Verlag,Berlin, 1987. 17.

Zhang Xiao-yong: Department of Mathematics, Shanghai Maritime University, Haigang Avenue, 1550, Shanghai,201306, China

Wan Zheng-su: Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China


202 Existence Results for Nonlinear Impulsive Fractional Dif-ferential Equations with p− Laplacian OperatorIlkay Yaslan Karaca and Fatma Tokmak

This paper is concerned with the existence of solutions for a nonlinear boundary value problem of impulsive fractional dif-ferential equations with p-Laplacian operator. By applying some standard fixed point theorems, obtain sufficient conditionsfor the existence of solutions of the problem at hand. Examples are presented to demonstrate the applicability of our results.

References[1] R. P. Agarwal, M. Belmekki and M. Benchohra, A survey on semilinear differential equations and inclusions involving

Riemann-Liouville fractional derivative, Adv. Difference Equ. 2009 Art. ID 981728 (2009) 47 pp.

[2] R. P. Agarwal and B. Ahmad, Existence of solutions for impulsive anti-periodic boundary value problems of fractionalsemilinear evolution equations, Dyna. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 18 (2011) 457-470.

[3] B. Ahmad and S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractionalorder, Nonlinear Anal.: Hybrid Syst. 4 (2010) 134-141.

[4] I. Y. Karaca, On positive solutions for fourth-order boundary value problem with impulse, J. Comput. Appl. Math. 225(2009) 356-364.

[5] I. Y. Karaca and F. Tokmak, Existence of solutions for nonlinear impulsive fractional differential equations with p-Laplacian operator, Mathematical Problems in Engineering 2014 Art. ID 692703 (2014) 11 pp.

[6] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier,Amsterdam, 2006.

[7] G. Wang, B. Ahmad and L. Zhang, Some existence results for impulsive nonlinear fractional differential equations withmixed boundary conditions, Comput. Math. Appl. 62 (2011) 1389-1397.

[8] G. Wang, W. Liu and C. Ren, Existence of solutions for multi-point nonlinear differential equations of fractional orderswith integral boundary conditions, Electron. J. Differential Equations 54 (2012) 10 pp.

[9] G. Wang, B. Ahmad and L. Zhang, New existence results for nonlinear impulsive integro-differential equations offractional order with nonlocal boundary conditions, Nonlinear Stud. 20 (2013) 119-130.

Ilkay Yaslan Karaca: Department of Mathematics, Ege University, Bornova, Izmir, Turkey, [email protected] Tokmak: Department of Mathematics, Gazi University, 06500 Teknikokullar, Ankara, Turkey, fatmatokmak

@gazi.edu.tr


203 A Relation Between the Lefschetz Fixed Point Theoremand the Nielsen Fixed Point Theorem in Digital ImagesIsmet Karaca

We present the Nielsen fixed point theorem for digital images. We deal with some important properties of the Nielsennumber and calculate the Nielsen number for some digital images. Finally, we give a relation between the Lefschetz fixedpoint theorem and the Nielsen fixed point theorem in digital images.

References[1] H. Arslan, I. Karaca, and A. Oztel, Homology groups of n-dimensional digital images XXI. Turkish National

Mathematics Symposium 2008, B1-13.

[2] L. Boxer, Digitally continuous functions, Pattern Recognition Letters 15(1994), 833-839.

[3] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vis. 10(1999), 51-62.

[4] L. Boxer, Properties of digital homotopy, Journal of Mathematical Imaging and Vision 22(2005), 19-26.

[5] L. Boxer, Homotopy properties of sphere-like digital images, Journal of Mathematical Imaging and Vision24(2006), 167-175.

[6] L. Boxer, Digital products, wedges and covering spaces, Journal of Mathematical Imaging and Vision 25(2006),169-171.

[7] L. Boxer and I. Karaca, The classification of digital covering spaces. J. Math. Imaging Vis.32, 23–29 (2008).

[8] L. Boxer and I. Karaca, Some properties of digital covering spaces. J. Math. Imaging Vis.37, 17-26 (2010).

[9] L. Boxer, I. Karaca, and A. Oztel, Topological invariants in digital images, Journal of Mathematical Sciences:Advances and Applications 11(2011)(2), 109-140.

[10] O. Ege and I. Karaca, Fundamental properties of digital homology groups, American Journal of ComputerTechnology and Application, 1(2), pp.25-42 (2013).

[11] O. Ege and I. Karaca, the Lefschetz Fixed Point Theorem for Digital Images, Preprint (2013).

[12] S.E. Han, Non-product property of the digital fundamental group. Inf. Sci. 171, 7-91 (2005).

[13] G.T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models and Image Processing 55(1993),381-396.

[14] I. Karaca and O. Ege, Some results on simplicial homology groups of 2D digital images, International Journalof Information and Computer Science 1(2012) no.8, 198-203.

[15] E. Khalimsky, Motion, deformation, and homotopy in finite spaces. In: Proceedings IEEE InternationalConference on Systems, Man, and Cybernetics, pp.227-234 (1987).

[16] J.R. Munkres, Elements of Algebraic Topology, Addison-Wesley Publishing Company, (1984).

[17] E. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).

Departments of Mathematics, Ege University Bornova Izmir, 35100 Turkey, [email protected]


204 Second Order Nonlinear Boundary Value Problems withIntegral Boundary Conditions on Time ScalesF.Serap Topal and Arzu Denk Oguz

This study investigates the existence of symmetric positive solutions for a class of nonlinear boundary value problem ofsecond order dynamic equations with integral boundary conditions on time scales. Under suitable conditions, the existence ofsymmetric positive solutions are established by using monotone iterative technique. An example is presented to demonstratethe application of our main result.

References[1] Y. Li, T. Zhang, Multiple positive solutions for second-order p-Laplacian dynamic equations with integral boundary

conditions. Bound. Value Probl., Article ID 867615 (2011)

[2] A.Boucherif, Second-order boundary value problems with integral boundary conditions, Non-linear Analysis, 70, 364-371(2009)

[3] M. Benchohra, J.J. Nieto, Abdelghani Ouahab, Second-Order Boundary Value Problem with Integral Boundary Condi-tions, Boundary Value Problems, Article ID 260309 (2011)

Ege University, Faculty of Science, Department of Mathematics, Bornova Izmir-Turkiye, [email protected]


205 Existence of a Solution of Integral Equations via FixedPoint TheoremSelma Gulyaz

In this talk, we establish a solution to the following integral equation

u(t) =

∫ T

0G(t, s)f(s, u(s)) ds, for all t ∈ [0, T ],

where T > 0, f : [0, T ]× R→ R and G : [0, T ]× [0, T ]→ [0,∞) are continuous functions. For this purpose, we also obtainsome auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.

References[1] Alghamdi, MA, Hussain, N, Salimi, P: Fixed point and coupled fixed point theorems on b-metric-like spaces. J. Inequal.

Appl. 2013, 402 (2013)

[2] Harandi, AA, Emami, H: A fixed point theorem for contraction type maps in partially ordered metric spaces andapplication to ordinary differential equations. Nonlinear Anal. 72, 2238-2242 (2010)

[3] Nieto, JJ, Lopez, RR: Contractive mapping theorems in partially ordered sets and applications to ordinary differentialequations. Order 22, 223-239 (2005)

[4] Harjani, J, Sadarangani, K: Fixed point theorems for weakly contractive mappings in partially ordered sets. NonlinearAnal. 71, 3403-3410 (2009)

[5] Moradi, S, Karapinar, E, Aydi, H: Existence of solutions for a periodic boundary value problem via generalized weaklycontractions. Abstr. Appl. Anal. 2013, Article ID 704160 (2013)

[6] Nahsine, HK: Cyclic generalized ψ-weakly contractive mappings and fixed point results with applications to integralequations. Nonlinear Anal. 75, 6160-6169 (2012)

[7] Karapinar, E, Shatanawi, W: On weakly (C,ψ, φ)-contractive mappings in partially ordered metric spaces. Abstr.Appl.Anal. 2012, Article ID 495892 (2012)

[8] Karapinar, E, Yuce, IS: Fixed point theory for cyclic generalized weak φ-contraction on partial metric spaces. Ab-str.Appl. Anal. 2012, Article ID 491542 (2012)

[9] Karapinar, E: Best proximity points of Kannan type cyclic weak φ-contractions in ordered metric spaces. An. Univ.gOvidiush ConstanCta, Ser. Mat. 20(3), 51-64 (2012)

[10] Karapinar, E: Best proximity points of cyclic mappings. Appl. Math. Lett. 25(11), 1761-1766 (2012)

Department of Mathematics, Cumhuriyet University, Sivas, Turkey, [email protected]


206 Triangular and Square Triangular NumbersArzu Ozkoc

In this work, we obtain some algebraic identities on triangular numbers denoted by Tn and square triangular numbersdenoted by Sn. And also we construct a connection between triangular and square triangular numbers. We determine whenthe equality Tm = Sn holds by using sn and tn denote the sides of the corresponding square and triangle respectively. Wederive some formulas on perfect squares, divisibility properties, sums of sn, tn, Sn, Tn and Pythagorean triples.

References[1] A. Behera and G.K. Panda. On the Square Roots of Triangular Numbers. The Fibonacci Quarterly, 37(2)(1999),

98-105.

[2] G.K. Panda. Some Fascinating Properties of Balancing Numbers. Proceedings of the Eleventh International Conferenceon Fibonacci Numbers and their Applications, Cong. Numer. 194(2009), 185–189.

[3] G.K. Panda and P.K. Ray. Some Links of Balancing and Cobalancing Numbers with Pell and Associated Pell Numbers.Bul. of Inst. of Math. Acad. Sinica 6(1)(2011), 41–72.

[4] P.K. Ray. Balancing and Cobalancing Numbers. PhD thesis, Department of Mathematics, National Institute of Tech-nology, Rourkela, India, 2009.

[5] S.F. Santana and J.L. Diaz–Barrero. Some Properties of Sums Involving Pell Numbers. Missouri Journal of Mathe-matical Science 18(1)(2006), 33–40.

Duzce University, Faculty of Arts and Science, Department of Mathematics, Konuralp, Duzce - Turkiye, [email protected]


207 Approximation Methods on a Complete Geodesic SpaceYasunori Kimura

In this talk, we propose iterative methods to approximate a common fixed point of mappings defined on a completegeodesic space with curvature bounded above. We also consider calculation error when generating an iterative sequence andwe observe its convergence property.

References[1] M. R. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wis-

senschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999.

[2] Y. Kimura, Approximation of a common fixed point of a finite family of nonexpansive mappings with nonsummableerrors in a Hilbert space, J. Nonlinear Convex Anal. 15 (2014), 429–436.

[3] Y. Kimura, A shrinking projection method for nonexpansive mappings with nonsummable errors in a Hadamard space,Ann. Oper. Res., to appear.

[4] Y. Kimura and K. Sato, Two convergence theorems to a fixed point of a nonexpansive mapping on the unit sphere of aHilbert space, Filomat 26 (2012), 949–955.

[5] W. Takahashi, Y. Takeuchi, and R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansivemappings in Hilbert spaces, J. Math. Anal. Appl. 341 (2008), 276–286.

Toho University, Faculty of Science, Department of Information Science, 2-2-1, Miyama, Funabashi, Chiba 274-8510,Japan, [email protected]


208 Fixed Point Results for α-Admissible Multivalued F−Cont-ractionsGonca Durmaz and Ishak Altun

In this study, we give some fixed point results for multivalued mappings using Pompeiu-Hausdorff distance on competemetric space. For this, we consider the α-admissibility of multivalued mappings. Our results are real generalizations ofMizoguchi-Takahashi fixed point theorem. We also provide an example showing this fact.

References[1] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications,

Springer, New York, 2009.

[2] I. Altun, G. Mınak and H. Dag, Multivalued F -Contractions On Complete Metric Space, Journal of Nonlinear andConvex Analysis, In press.

[3] V. Berinde and M. Pacurar, The role of the Pompeiu-Hausdorff metric in fixed point theory, Creat. Math. Inform., 22(2) (2013), 35-42.

[4] Lj. B. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Anal., 71 (2009), 2716-2723.

[5] D. Klim and D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal.Appl., 334 (2007), 132-139.

[6] G. Mınak and I. Altun, Some new generalizations of Mizoguchi-Takahashi type fixed point theorem, Journal of In-equalities and Applications, 2013, 2013:493.

[7] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math.Anal. Appl.,141 (1989), 177-188.

[8] S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 4 (5) (1972), 26-42.

[9] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point TheoryAppl. 2012, 2012:94, 6 pp.

[10] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis 75(2012), 2154-2165.

[11] E. Karapınar and B. Samet, Generalized α-ψ-contractive type mappings and related fixed point theorems with appli-cations, Abstract and Applied Analysis 2012 (2012), Article ID 793486, 17 pages.

[12] J.H. Asl, S. Rezapour and N. Shahzad, On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory andApplications 212 (2012), 6 pages, doi:10.1186/1687-1812-2012-212..

[13] H. Nawab, E. Karapınar, P. Salimi and F. Akbar, α-admissible mappings and related fixed point theorems, Journal ofInequalities and Applications 114 (2013), 11 pages.

Gonca Durmaz: Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan,Kirikkale, Turkey, [email protected]

Ishak Altun: Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale,Turkey, [email protected]


209 Advances on Fixed Point TheoryErdal Karapınar

In this talk, we discuss on the advances on metric fixed point theory and some other abstract spaces via the recentpublications on the topics. In particular, we point out the extension and improvement in various abstract spaces, such asgeneralized metric space.

References[1] R. Agarwal and E. Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory

and Applications (2013), 2013:2

[2] R.P.Agarwal, E. Karapinar, A.Roldan, Fixed point theorems in quasi-metric spaces and applications to multidimensionalfixed point theorems on G-metric spaces, Journal of Nonlinear and Convex Analysis

[3] E. Karapinar and R.P. Agarwal, Further fixed point results on G-metric spaces, Fixed Point Theory and Applications,1 (2013) 2013:154

Atilim University, Department of Mathematics, Incek,Ankara Turkey [email protected], erdalkarapinar @ya-hoo.com


210 Fixed Point Theorems for a Class of α-Admissible Con-tractions and Applications to Boundary Value ProblemInci M.Erhan

In this talk, we introduce a class of α-admissible contraction mappings defined via altering distance functions and actingon complete metric spaces. We investigate conditions for the existence and uniqueness of fixed points for these contractionsand discuss the results in partially ordered spaces. As an application, we consider boundary value problems for a first orderdifferential equations with periodic boundary conditions.

References[1] R. P. Agarwal, M. A. El- Gebeily and D. O’Regan Generalized contractions in partially ordered metric spaces, Appl.

Anal., 87, 1–8, (2008).

[2] T. G. Bhaskar and V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applicaitons, NonlinearAnalysis, 65, 1379–1393, (2006).

[3] V. Lakshmikantham and Lj. B. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metricspaces, Nonlinear Analysis, 70, 4341–4349, (2009).

[4] H. K. Nashine and B. Samet, Fixed point results for mappings satisfying (ψ, φ) weakly contractive condition in partiallyordered metric spaces, Nonlinear Analysis, 74, 2201–2209, (2011).

Atılım University, Department of Mathematics, 06530, Incek Ankara-Turkiye, [email protected]


211 Feng-Liu Type Fixed Point Theorems for Multivalued Map-pingsGulhan Mınak and Ishak Altun

In this talk, considering the recent technique, which is used by Jleli and Samet for fixed points of single valued mappings, wegive some results of fixed points for multivalued mappings on complete metric space. Our results are proper generalizationsof some related fixed point theorems including the famous Feng-Liu’s result in the literature. We also give some examplesto both illustrate and show that our results are real generalizations of mentioned theorems.

References[1] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications,

Springer, New York, 2009.

[2] M. Berinde and V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326(2007), 772-782.

[3] Lj. B. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Anal., 71 (2009), 2716-2723.

[4] Y. Feng and S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings,J. Math. Anal. Appl., 317 (2006), 103-112.

[5] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math.Anal. Appl.,141 (1989), 177-188.

[6] S.B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.

[7] S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 4 (5) (1972), 26-42.

[8] T. Suzuki, Mizoguchi-Takahashi’s fixed point theorem is a real generalization of Nadler’s, J. Math. Anal. Appl., 340(2008), 752-755.

[9] M., Jleli and B. Samet, A new generalization of the Banach contraction principle, Journal of Inequalities and Applications2014, 2014:38 8 pp.

Ishak Altun: Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale,Turkey, [email protected]

Gulhan Mınak: Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan,Kirikkale, Turkey, [email protected]


212 Qualitative Analysis for the Differential Equation Associ-ated to the Dynamic Model for an Access Control StructureDaniela Coman, Adela Ionescu and Sonia Degeratu

This paper presents some analytical considerations regarding the dynamical behavior of an access control structure, basedon the mathematical model associated to this structure.

This structure type is large analyzed in the literature. A modern approach of this structure based on SMA (shapememory alloy) is taken into account, because of some particular advantages due: unique characteristics (superelastic effect,as well as the single and double shape memory effects), damping capacity of noise and vibration, simplify and lower weightstructure, high resistance to corrosion and wear, resistance to fatigue (which can occur even after hundreds of thousands ofcycles), diversification of the control and command possibilities.

The qualitative analysis of the mathematical model associated to this structure is taken into account. Namely, thedifferential equation associated to the variation of the angle describing the position of the access control structure isanalyzed from the influence of parameters standpoint. The MAPLE11 soft is used in order to evaluate the behavior of theequation solution with respect to the parameters variation.

This analysis produces a data collection which is useful both for further developing a fuzzy logic controller for the activecontrol of this access structure and for further refinements of the mathematical model associated to this structure type

References[1] M.L. Abell, J.P. Braselton,Maple by Example, 3rd edition. Elsevier Academic Press, San Diego, California (2005)

[2] S. Degeratu, P. Rotaru, S. Rizescu, N.G. Bizdoaca, Thermal study of a shape memory alloy (SMA) spring actuatordesigned to insure the motion of a barrier structure, Journal of Thermal Analysis and Calorimetry, 111 (2013), 1255–1262

[3] S. Degeratu, N.G. Bizdoaca, S. Rizescu, P. Rotaru, V. Degeratu, G. Tont, Barrier structures using shape memory alloysprings, Proceedings of the International Conference on Development, Energy, Enviroment, Economics (DEEE ’10),367-372

[4] N.G. Bizdoaca, A. Petrisor, S. Degeratu, P. Rotaru, E. Bizdoaca , Fuzzy logic controller for shape memory alloy ten-dons actuated biomimetic robotic structure, International Journal on Automation, Robotics and Autonomous Systems(ARAS), Issue II, vol. 09 (2009), 27-34

Daniela Coman: Department of Engineering and Management of Technological Systems, Faculty of Mechanics, Univer-sity of Craiova, Calugareni Str no1, 220037 , Romania, [email protected]

Adela Ionescu: Department of Applied Mathematics, University of Craiova, Al. I. Cuza 13, Craiova 200585, Romania,[email protected]

Sonia Degeratu: Faculty of Automatics, Department of Electromechanics, 107 Decebal Blvd., 200440, University ofCraiova, Romania, [email protected]

This work was partially supported by the grant number 7C/2014, awarded in the internal grant competition of theUniversity of Craiova.


213 Zagreb Indices of Double GraphsAysun Yurttas, Muge Togan and Ismail Naci Cangul

In this presentation, authors will give some new results and inequalities on several types of Zagreb indices for double graphs.

References[1] K. C. Das, N. Trinajstic, Relationship Between the Eccentric Connectivity Index and Zagreb Indices, Comp. Math.

Appl., 62 (4) (2011), 1758-1764

[2] I. Gutman, K. C. Das, The First Zagreb Index 30 Years After, MATCH Commun. Math. Comput. Chem. 50 (2004),83-92

[3] P. S. Ranjini, V. Lokesha, I. N. Cangul, On the Zagreb Indices of the Line Graphs of the Subdivision Graphs, Appl.Math. Comput., 218 (2011), 699-702

[4] M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The First and Second Zagreb Indices of some Graph Operations,Discrete Appl. Math., 157 (2009), 804-811

[5] K. Ch. Das, A. Yurttas, M. Togan, I. N. Cangul, A. S. Cevik, The multiplicative Zagreb indices of graph operations,Journal of Inequalities and Applications, 90, (2013)

[6] I. Gutman, Multiplicative Zagreb indices of trees, Bulletin of Society of Mathematicians Banja Luka, 18 (2011), 17-23

[7] M. Togan, A. Yurttas, I. Naci Cangul, All versions of Zagreb indices and coindices of subdivision graphs of certain graphtypes (submitted)

[8] M. Togan, A. Yurttas, I. Naci Cangul, All versions of Zagreb indices and coindices of r-subdivision graphs of certaingraph types (submitted)

[9] M. Togan, A. Yurttas, I. Naci Cangul, Zagreb indices and multiplicative Zagreb indices of subdivision graphs of doublegraphs for several graph types (submitted)

Uludag University, Department of Mathematics, Gorukle 16059 Bursa, Turkey, [email protected], [email protected], [email protected]

The authors are supported by the Commission of Scientific Research Projects of Uludag University, project numbers2012/15, 2012/19, 2012/20 and 2013/23.


214 Several Zagreb Indices of Subdivision Graphs of DoubleGraphsMuge Togan, Aysun Yurttas and Ismail Naci Cangul

In this presentation, authors study the subdivision graphs of the double graphs of certain graph types and give some newresults and inequalities on several types of Zagreb indices for subdivision graphs of double graphs.

References[1] K. C. Das, N. Trinajstic, Relationship Between the Eccentric Connectivity Index and Zagreb Indices, Comp. Math.

Appl., 62 (4) (2011), 1758-1764

[2] I. Gutman, K. C. Das, The First Zagreb Index 30 Years After, MATCH Commun. Math. Comput. Chem. 50 (2004),83-92

[3] P. S. Ranjini, V. Lokesha, I. N. Cangul, On the Zagreb Indices of the Line Graphs of the Subdivision Graphs, Appl.Math. Comput., 218 (2011), 699-702

[4] M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The First and Second Zagreb Indices of some Graph Operations,Discrete Appl. Math., 157 (2009), 804-811

[5] K. Ch. Das, A. Yurttas, M. Togan, I. N. Cangul, A. S. Cevik, The multiplicative Zagreb indices of graph operations,Journal of Inequalities and Applications, 90, (2013)

[6] I. Gutman, Multiplicative Zagreb indices of trees, Bulletin of Society of Mathematicians Banja Luka, 18 (2011), 17-23

[7] M. Togan, A. Yurttas, I. Naci Cangul, All versions of Zagreb indices and coindices of subdivision graphs of certain graphtypes (submitted)

[8] M. Togan, A. Yurttas, I. Naci Cangul, All versions of Zagreb indices and coindices of r-subdivision graphs of certaingraph types (submitted)

[9] M. Togan, A. Yurttas, I. Naci Cangul, Zagreb indices and multiplicative Zagreb indices of subdivision graphs of doublegraphs for several graph types (submitted)

Uludag University, Department of Mathematics, Gorukle 16059 Bursa, Turkey, [email protected], [email protected], [email protected]

The authors are supported by the Commission of Scientific Research Projects of Uludag University, project numbers2012/15, 2012/19, 2012/20 and 2013/23.


215 On the Solutions of the Diophantine Equation xn + p · yn =p2 · znCaner Agaoglu and Musa Demirci

In this paper we considered the Diophantine equation

xn + p · yn = p2 · zn (215.1)

when n ≥ 2 and x, y, z are positive integers. Some special cases of (215.1) was already undertaken in the literature. Ingeneral form (215.1) we used Fermat’s Method of Infinite Descent (FMID) to determine the existence of solutions.

References[1] Andreescu T., Andrica D., Cucurezeanu I., “An introduction to Diophantine Equations” , Springer, 2010, ISBN

978-0-8176-4549-6.

[2] Powell B. J.,“Proof of the Impossibility of the Fermat Equation xp + yp = zP for Special Values of p and of MoreGeneral Equation b · xn + c · yn = d · zn”, Journal of Number Theory 18 (1984), 34-40.

[3] Manley S., “On Quadratic Solutions of x4 + p · y4 = z4”, Rocky Mountain Journal of Mathematics, 36-3 (2006),1027-1031.

Uludag University, Faculty of Science, Department of Mathematics, Bursa-Turkey, [email protected]


216 A Weak Contraction Principle in Partially Ordered ConeMetric Space with Three Control FunctionsBinayak S.Choudhury, L.Kumar, T.Som and N.Metiya

In this paper we utilize three functions to define a weak contraction in a cone metric space with a partial order and establishthat this contraction has necessarily a fixed point either under the continuity assumption or an order condition which westate here. The uniqueness of the fixed point is also derived under some additional assumptions. The result is supportedwith an example. The methodology used is a combination of order theoretic and analytic approaches.

Binayak S.Choudhury: Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, West Bengal, India, [email protected], [email protected]

L.Kumar: Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi-221005, India, [email protected]

T.Som: Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi-221005, India, [email protected]

N.Metiya: Department of Mathematics, Bengal Institute of Technology, Kolkata - 700150, West Bengal, India, [email protected]


217 On the Diophantine Equation (20n)x + (99n)y = (101n)z

Gokhan Soydan, Musa Demirci and Ismail Naci Cangul

For a positive integer n, the triple (a, b, c) with a = u2 − v2, b = 2uv, c = u2 + v2, u > v > 0, 2 | uv, (u, v) = 1 satisfiesa2 + b2 = c2. There are conjectures and results on

(an)x + (bn)y = (cn)z (217.1)

with x, y, z ∈ Z+. (x, y, z) = (2, 2, 2) satisfies (217.1). In 1956, Sierpinski, [6], showed that (217.1) has no other solutionwhen n = 1 and (a, b, c) = (3, 4, 5) and Jesmanowicz, [3], proved that when n = 1 and (a, b, c) = (5, 12, 13), (7, 24, 25),(9, 40, 41), (11, 60, 61), only solution is (x, y, z) = (2, 2, 2). He conjectured that (217.1) has no positive integer solutionsother than (x, y, z) = (2, 2, 2). In 1959, Lu, [5], proved that (217.1) has the unique solution (x, y, z) = (2, 2, 2) if n = 1and (a, b, c) = (4k2 − 1, 4k, 4k2 + 1). In 1998, Deng and Cohen, [1], proved that Jesmanowicz conjecture is true for(a, b, c) = (3, 4, 5). In 1999, Le, [4], gave certain conditions for (217.1) to have positive integer solutions (x, y, z) with(x, y, z) 6= (2, 2, 2). Recently several authors showed that Jesmanowicz conjecture is true with 2 ≤ k ≤ 4 and k = 8. In2013, Tang and Yang, [7], dealt with the case k = 2 and Deng, [2], also wrote a general paper covering this case. In 2012,Zhijuan and Jianxin, [9], discussed the case k = 3. Deng, [2], studied the case k = 2s, 1 ≤ s ≤ 4 and this covers the casek = 4. Finally the case k = 8 is covered by Tang and Weng, [8], where the authors considered a special case (n = 3) that c

is a Fermat number c = Fn = 22n + 1, a = Fn − 2 and b = 22n−1+1 for n ≥ 1. Next we consider (217.1) with k = 5. Weconsider (217.1) with (a, b, c) = (20, 99, 101) and conclude that (217.1) has no solution other than (x, y, z) = (2, 2, 2).

References[1] M. J. Deng, G. L. Cohen, “On the conjecture of Jesmanowicz’ concerning Pythagorean triples”, Bull. Aust. Math. Soc.

57 (1998), 515–524.

[2] M. J. Deng, “A note on the Diophantine equation (na)x + (nb)y = (nc)z”, Bull. Aust. Math. Soc. (2013), to appear.

[3] L. Jesmanowicz, “Several remarks on Pythagorean numbers”, Wiadom. Math. 1 (1955/56), 196–202.

[4] M. H. Le, “A note on Jesmanowicz’ conjecture concerning Pythagorean triples”, Bull. Aust. Math. Soc. 59 (1999),477–480.

[5] W. D. Lu, “On the Pythagorean numbers 4n2 − 1, 4n and 4n2 + 1”, Acta Sci. Natur. Univ. Szechuan 2 (1959), 39–42.

[6] W. Sierpinski, “On the equation 3x + 4y = 5z”, Wiadom. Math. 1 (1955/56), 194–195.

[7] M. Tang, Z. J. Yang, “Jesmanowicz’ conjecture revisited”, Bull. Aust. Math. Soc. 88 (2013), 486–491.

[8] M. Tang, J. X. Weng, “Jesmanowicz’ conjecture revisited-II”, Bull. Aust. Math. Soc. (2013), to appear.

[9] Y. Zhijuan, W. Jianxin, “On the Diophantine equation (12n)x + (35n)y = (37n)z”, Pure and App. Math.(Chinese) 28(2012), 698–704.

Department of Mathematics, Uludag University, 16059 Bursa, Turkey, [email protected], [email protected],[email protected]


218 Halpern Type Iteration with Multiple Anchor Points in aHadamard SpaceYasunori Kimura and Hideyuki Wada

In this talk, we consider an approximation theorem of common fixed points of nonexpansive mappings in a Hadamard space.Saejung [2] obtained that a Halpern type iteration with a nonexpansive mapping converges strongly to the fixed point in aHadamard space. We introduce that another style of Halpern type iteration with multiple nonexpansive mappings convergesstrongly to the common fixed point in a Hadamard space. Kimura, Takahashi and Toyoda [1] proved the approximationof common fixed points of a finite family of nonexpansive mappings in a uniformly convex Banach space whose norm isGateaux differentiable. We obtain the main result under similar conditions of theirs. In the known results, the anchor pointof Halpern type iteration is single, however the anchor points of our iterative sequence are multiple.

References[1] Y. Kimura, W. Takahashi, M, Toyoda, Convergence to common fixed points of a finite family of nonexpansive mappings,

Arch. Math. (Basel) 84 (2005), 350–363.

[2] S. Saejung, Halpern’s Iteration in CAT(0) Spaces, Fixed Point Theory and Appl. 2010 (2010), 13pp.

[3] R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. (Basel) 58 (1992), 486–491.

Yasunori Kimura: Toho University, Department of Information Science, 2-2-1, Miyama, Funabashi, Chiba 274-8510,Japan, [email protected]

Hideyuki Wada: Toho University, Graduate School of Science, Department of Information Science, 2-2-1, Miyama,Funabashi, Chiba 274-8510, Japan, [email protected]


219 Multimaps in Fixed Point Theorems in Terms of Measureof NoncompactnessMehdi Asadi

We present some of fixed point theorems for multimaps in fixed point theory and applications on measure of noncompactness.The main results are formulated in terms of definition of measure of noncompactness. Our theorems extend in a broad sensesome new and classical results.

Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran, [email protected]


220 Pointwise Approximation in Lp Space by Double SingularIntegral OperatorsMine Menekse Yılmaz, Gumrah Uysal and Ertan Ibikli

In this talk, we will prove the pointwise approximation of Lλ (f, x, y) to f (x0, y0) , as (x, y, λ) tends to (x0, y0, λ0) smallin the space Lp by double singular integral operators at the characteristic point.

References[1] A. D.Gadjiev, On the order of convergence of singular integrals which depending on two parameters. Special Prob. of

Funct. Analysis and its Appl. to the Theory of D. E. and the Theory of Funct. Izdat. Akad. Nauk Azerbaıdazan, Baku,(1968), 40–44.

[2] H. Karsli, and E. Ibikli, On convergence of convolution type singular integral operators depending on two parameters,Fasc. Math. 38 (2007), 25–39.

[3] R.J. Nessel, Contributions to the theory saturation for singular integrals in several variables, III, radial kernels. Indag.Math. 29. Ser. A. (1965), 65-73.

[4] S. A. Stanislaw, Theorem of Romanovski type for double singular integrals. Comment. Math. 29.(1986), 277-289.

[5] R. Taberski, On double integrals and Fourier Series. Ann. Pol. Math. (1964), 97-115.

[6] M.M. Yilmaz, On convergence of Singular Integral Operators Depending on Three Parameters with Radial Kernels, Int.Journal of Math. Analysis, 4, (2010), no 39, 1923-1928.

Mine Menekse: Gaziantep University, Faculty of Arts and Science, Department of Mathematics, Gaziantep, Turkey,[email protected]

Gumrah Uysal: Karabuk University, Faculty of Science, Department of Mathematics, Balıklarkayası Mevkii, Karabuk,Turkey, [email protected]

Ertan Ibikli: Ankara University, Faculty of Science, Department of Mathematics, Tandogan, Ankara, Turkey, [email protected]


221 Some Tauberian Remainder Theorems for Iterations ofWeighted Mean Methods of SummabilitySefa Anıl Sezer and Ibrahim Canak

In this study, our aim is to retrieve λ−boundedness of a real sequence from its λ−boundedness by (N, p, k) summabilitymethod. To that end, we provide several Tauberian remainder theorems for the (N, p, k) summability method using thegeneral control modulo of the oscillatory behavior given by Dik [2].

References[1] I. Canak and U. Totur. Some Tauberian theorems for the weighted mean methods of summability. Comput. Math.

Appl., 62(6) (2011), 2609–2615,

[2] M. Dik. Tauberian theorems for sequences with moderately oscillatory control moduli. Math. Morav., 5 (2001), 57–94,

[3] G. Kangro. A Tauberian remainder theorem for the Riesz method. Tartu Riikl. Ul. Toimetised, 277 (1971), 155–160,

[4] O. Meronen and I. Tammeraid. Generalized Norlund method and convergence acceleration. Math. Model. Anal., 12(2)(2007), 195–204,

[5] O. Meronen and I. Tammeraid. Several theorems on λ-summable series. Math. Model. Anal., 15(1) (2010), 97–102,.

[6] O. Meronen and I. Tammeraid. General control modulo and Tauberian remainder theorems for (C, 1) summability.Math. Model. Anal., 18(1) (2013), 97–102,

[7] A. Seletski and A. Tali. Comparison of speeds of convergence in Riesz-type families of summability methods. II. Math.Model. Anal., 15(1) (2010), 103–112,

[8] S. A. Sezer and I. Canak. Tauberian Remainder Theorems for the Weighted Mean Method of Summability. Math.Model. Anal., 19(2) (2014), 275–280,

[9] U. Totur and I. Canak. Some general Tauberian conditions for the weighted mean summability method. Comput. Math.Appl., 63(5) (2012), 999–1006.

Sefa Anıl Sezer: Ege University, Faculty of Science, Department of Mathematics, Izmir-Turkey and IstanbulMedeniyet University, Faculty of Science, Department of Mathematics, Istanbul-Turkey, [email protected] or [email protected]

Ibrahim Canak: Ege University, Faculty of Science, Department of Mathematics, Izmir-Turkey, [email protected]


222 On The Semi-Fredholm SpectrumArzu Akgul

In this talk, a version of semi Fredholm joint spectrum for families of noncommuting operators is defined. Moreover, byusing homological methods and the connections between Fredholm joint spectrum and upper-semi Fredholm and lower –semiFredholm spectrum , spectral mapping theorem is proved and some propertiesof semi Fredholm spectrum are investigated.

References[1] Atkinson, Multiparameter Eingen Value Problems, New York, 1968

[2] Dosiyev, A. Spectra of Infinte Parametrized Banach Complexes, Journal of Operator Theory, 48, 2002, no.3, 585-614

[3] Fainshtein A.S., Taylor Joint Spectrum for Families of Operators Generating Nilpotent Lie algebras. Journal of OperatorTheory,29. 1993, 2-27

[4] Taylor, J.L. A joint Spectrum for Several Commuting Operators, Journal of Functional Analysis, v.26 ,1970, , 12-72.

Kocaeli University, Faculty of Science and Arts, Department of Mathematics, Kocaeli, [email protected]


223 Critical Fixed Point Theorems in Banach Algebras UnderWeak Topology FeaturesA.Ben Amar and A.Tlili

In this paper we prove some new fixed point theorems for weakly sequentially continuous operators of type x = AxBx+Cx ina Banach algebra. For this purpose, we introduce the concept of multi-valued mappings under conditions of weak topology.We also provide some new results concerning the sum and the product of nonlinear weakly sequentially continuous mappingsin a Banach algebra satisfying a certain sequential condition (P).

References[1] R. E. Edwards, Functional analysis, Theory and applications. Holt. Rein. Wins. New York, (1965).

[2] A. Ben Amar, A. Jeribi and M. Mnif, On a generalization of the Schauder and Krasnoselskii fixed point theorems andapplication to biological model. Number. Funct. Anal. Optim., 29 (1), 1-23, (2008).

[3] A. Ben Amar and M. Mnif, Leary-Schauder alternatives for weakly sequentially continuous mappings and applicationto transport equation. Math. Methods Appl. Sci., 33, 80-90, (2010).

[4] A. Ben Amar and A. Sikorska-Nowak, On some fixed point theorems for 1-weakly contractive multi-valued mappingswith weakly sequentially closed graph. preprint, (2010).

[5] D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969) 458-464.

[6] I. Dobrakov, On representation of linear operators on C Math. J. 21 (96) (1971) 13-30.

[7] B. C. Dhage, Multi-valued operators and fixed point theorems in Banach algebras I, Nonlinear functional anal and appl.,10(4) (2006), 1025-1045.

[8] E.Zeidler, Non linear functional analysis and applications. Vol. 1. Springer. New York (1986).


224 Modeling of Effect of the Components of Distance Educa-tion in Achievement of StudentsHamit Armagan, Tuncay Yigit and Ahmet Sahiner

Distance education is a kind of education that brought together course advisor,student and educational materials in adifferent time and place through commenicational technologies. In this educational system the success of education isdirectly related to audio, video and interaction. In this study,a model is created by using fuzzy logic with the success ofdistance education students and the components of distance education. In addition, with a global optimization method itis determined which are the highest student achievement points.

References[1] E. H. Mamdani, Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis, IEEE Trans.

Computers, 26(12) (1977),1182-1191.

[2] F. Esragh, E.H. Mamdani, A general approach to linguistic approximation, Fuzzy Reasoning and Its Applications,Academic Press,1981.

[3] E.H. Mamdani, Application of fuzzy algorithms for simple dynamic plant. Proc. IEE 121 (1974), 1585-1588.

[4] A. Sahiner, H. Gokkaya, N. Ucar, Nonlinear Modelling of the Layer Microhardnes of Fe-Mn Binory Allays, Journal ofBalkan Tribological Association, 4 (2013) ,508-519.

[5] A. Sahiner, I. Uney , M. F. Gurbuz, An Application of Fuzzy Logic in Entomology: Estimating the Egg Productionand Opening of Pimpla Turianellae L., IWBCMS-2013 Procoeding Book, 323-332.

[6] T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst.,Man, Cybern, 15 (1985), 116-132.

[7] L. A. Zadeh, Fuzzy Sets, Inf. Control, 8 (1965),338-353.

[8] Z.Y. Wu, H. W. J.Lee, L.S. Zhang, X. M. Yang, A Novel Filled Function Method and Quasi-Filled Function Methodfor Global Optimization, Comput. Optim. Appl., 34 (2005), 246-272 .

[9] L. A. Zadeh, Fuzzy Sets as a Basis for a Theory of Posibility, Fuzzy Sets Syst, 1 (1978), 3-28.

[10] L. A. Zadeh, The consept of a linguistic variable and its application to approximate reasoning I, Information Sciences,8(3) (1975), 199-249, (1975)

[11] Y. Lin, Y. Yang, L. Zhang, A Novel Filled Function Method for Global Optimization, J. Korean Math. Soc. 47(6)(2010), 1253-1267 .

[12] A. Sahiner, H. Gokkaya, T. Yigit, A new filled function for non-smooth global optimization, AIP Conf. Proc. 1479(2012), 972-974.

[13] S. Karagoz, H. Zulfikar, T. Kalayci, 2014. Ogrenme surecine ilisskin degerlendirmeler ve fuzzy karar verme teknigi ilesurece dair bir uygulama, Istanbul Universitesi Sosyal Bilimler Dergisi, (1) (2014),56-71.

Hamit Armagan: Suleyman Demirel University, Department of Information, Isparta/Turkiye, [email protected] Yigit: Suleyman Demirel University, Faculty of Engineering, Department of Computer Engineering, Is-

parta/Turkiye, [email protected] Sahiner: Suleyman Demirel University, Faculty of Art and Science, Department of Mathematics, Isparta/Turkiye,

[email protected]


225 On the Weighted Integral Inequalities for Convex FunctionMehmet Zeki Sarıkaya and Samet Erden

In this talk, we establish several weighted inequalities for some differantiable mappings that are connected with the celebratedHermite-Hadamard-Fejer type and Ostrowski type integral inequalities. The results presented here would provide extensionsof those given in earlier works.

References[1] F. Ahmad, N. S. Barnett and S. S. Dragomir, New Weighted Ostrowski and Cebysev Type Inequalities, Nonlinear

Analysis:

Theory, Methods & Appl., 71 (12), (2009), 1408-1412.

[2] F. Ahmad, A. Rafiq, N. A. Mir, Weighted Ostrowski type inequality for twice differentiable mappings, Global Journalof

Research in Pure and Applied Math., 2 (2) (2006), 147-154.

[3] N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality for double integrals and applications for cubatureformulae,

Soochow J. Math., 27(1), (2001), 109-114.

[4] N. S. Barnett, S. S. Dragomir and C.E.M. Pearce, A Quasi-trapezoid inequality for double integrals, ANZIAM J.,44(2003),

355-364.

[5] S. S. Dragomir, P. Cerone, N. S. Barnett and J.

Roumeliotis, An inequlity of the Ostrowski type for double integrals and applications for cubature formulae, TamsuiOxf. J. Math., 16(1),

(2000), 1-16.

[6] S. Hussain, M.A.Latif and M. Alomari, Generalized duble-integral Ostrowski type inequalities on time scales, Appl.Math.

Letters, 24(2011), 1461-1467.

[7] M. E. Kiris and M. Z. Sarikaya, On the new generalization of Ostrowski type inequality for double integrals,

International Journal of Modern Mathematical Sciences, 2014, 9(3): 221-229.

[8] L. Fejer, Uber die Fourierreihen, II. Math.

Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369–390. (Hungarian).

[9] U.S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers and to midpointformula, Appl. Math. Comp., 147 (2004), 137-146.

[10] A. M. Ostrowski, Uber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment.Math.

Helv. 10(1938), 226-227.

[11] J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press,

New York, 1991.

[12] A. Qayyum, A weighted Ostrowski-Gruss type inequality and applications, Proceeding of the World Cong. on Engi-neering,

Vol:2, 2009, 1-9.

[13] A. Rafiq and F. Ahmad, Another weighted Ostrowski-Gr uss type inequality for twice differentiable mappings, Kragu-jevac

Journal of Mathematics, 31 (2008), 43-51.

[14] M. Z. Sarikaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenianae, Vol. LXXIX, 1(2010), pp.129-134.

[15] M. Z. Sarikaya On the Ostrowski type integral inequality for double integrals, Demonstratio Mathematica, Vol. XLV,No 3,

pp:533-540, 2012.

Mehmet Zeki Sarıkaya: Duzce University, Faculty of Science and Arts, Department of Mathematics, Duzce-Turkiye,[email protected]

Samet Erden: Bartın University, Faculty of Science, Department of Mathematics, Bartın-Turkiye, [email protected]


[16] M. Z. Sarikaya and H. Ogunmez, On the weighted Ostrowski type integral inequality for double integrals, The Arabian

Journal for Science and Engineering (AJSE)-Mathematics, (2011) 36:1153-1160.

[17] M. Z. Sarikaya, On the generalized weighted integral inequality for double integrals, Annals of the Alexandru Ioan Cuza

University-Mathematics, accepted.

[18] M. Z. Sarikaya, On new Hermite Hadamard Fejer Type integral inequalities, Studia Universitatis Babes-Bolyai Math-ematica.,

57(2012), No. 3, 377-386.

[19] M. Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals,Submited

[20] K-L. Tseng, G-S. Yang and K-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequalityand weighted trapozidal formula, Taiwanese J. Math. 15(4),

pp:1737-1747, 2011.

[21] C.-L. Wang, X.-H. Wang, On an extension of Hadamard inequality for convex functions, Chin. Ann. Math. 3 (1982)567–570.

[22] S.-H. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, The Rocky Moun-tain J. of

Math., vol. 39, no. 5, pp. 1741–1749, 2009.


List of Participants1. A.A.Dosiyev: Eastern Mediterranean University

2. A.Laifa: Universite du 20 aout 1955-Skikdav

3. A.Lebaroud: Universite du 20 aout 1955-Skikda

4. A.Medoued: Universite du 20 aout 1955-Skikda

5. A.R.Aithal: University of Mumbai

6. A.R.Bindusree: Sree Narayana Gurukulam College of Engineering

7. A.Tatarczak: Maria Curie-Sklodowska University in Lublin

8. A.Turan Gurkanlı: Istanbul Arel University

9. Abdelmalek Mohammed: Ecole preparatoire en sciences economiques

10. Abdessalem Benammar: Welding and NDT Research Center (CSC)

11. Abdullah Cavus: Karadeniz Technical University

12. Abdullah Dertli: Ondokuz Mayıs University

13. Abdullah Ozbekler: Atilim University

14. Abdurrahman Dayioglu: Uludag University

15. Acushla Sarswat: University of Mumbai

16. Adela Ionescu: University of Craiova

17. Ademi Ospanova: L.N.Gumilyov Eurasian National University

18. Adnan Kılıc: Uludag University

19. Ahmed GhezalUniversity of Constantine 1

20. Ahmed Khechida: Welding and NDT Research Center (CSC)

21. Ahmet Emin: Balikesir University

22. Ahmet Sinan Cevik: Selcuk University

23. Ahmet Sahiner: Suleyman Demirel University

24. Ahu Acıkgoz: Balikesir University

25. Aiman Mukheimer: Prince Sultan University

26. Alen Osanclıol : SabancıUniversity

27. Ali Akgul: Dicle University

28. Ali Aral: Kirikkale University

29. Ali Demir: Kocaeli University

30. Anuj Kumar: Banaras Hindu University

31. Arzu Denk Oguz: Ege University

32. Arzu Akgul: Kocaeli University

33. Arzu Ozkoc: Duzce University

34. Aslı Ayten Kaya: Uludag University

35. Aydın Tiryaki: Izmir University

36. Aykut Ahmet Aygunes: University of Akdeniz

37. Aynur Sahin: Sakarya University

38. Aynur Yalcıner: Selcuk University

39. Aysun Yurttas: Uludag University

40. Ayse Feza Guvenilir: Ankara University

41. Ayse Sandıkcı: Ondokuz Mayıs University

42. Aysegul Akyuz-Dascıoglu: Pamukkale University

43. Ayten Pekin: Istanbul University

44. Aziz Halit Gozel: Adiyaman University

45. Basri Celik: Uludag University

46. Belmeguenai Aissa: Universite 20 Aout 1955-Skikda


47. Benmansour Safia: Ecole preparatoire en sciences economiques

48. Benmerai Romaissa: University of Constantine 1

49. Bilal Demir: Balikesir University

50. Bilel Mefteh: Sfax University

51. Billur Kaymakcalan: Cankaya University

52. Binayak S.Choudhury: Bengal Engineering and Science University

53. Boughazi Hichem: Preparatory School in Economics

54. Boumediene Abdellaoui: Universite Abou Bakr Belkaıd

55. Burcin Simsek: University of Pittsburgh

56. Burcu Ozturk: Trakya University

57. C.S.Ryoo: Hannam University

58. Can Murat Dikmen: Bulent Ecevit Universitesi

59. Caner Agoglu: Uludag University

60. Canybec Sulayman: University of California

61. Cengiz Akay: Uludag University

62. Chandrashekar Adiga: University of Mysore

63. Cetin Yıldız: Ataturk University

64. D.Azzam-Laouir: University of Jijel

65. D.Sayad: Universite du 20 aout 1955-Skikda

66. Daeyeoul Kim: National Institute for Mathematical Sciences

67. Dalila Azzam-Laouir: Universite de Jijel

68. Daniela Bımova: Technical University of Liberec

69. Daniela Bittnerova: Technical University of Liberec

70. Daniela Coman: University of Craiova

71. Dib Djalel: University of Tebessa

72. Djavvat Khadjiev: Karadeniz Technical University

73. Djezzar Salah: University of Constantine 1

74. Dmitry V.Kruchinin: Tomsk State University of Control Systems and Radioelectronics

75. Doria Affane: Universite de Jijel

76. Durhasan Turgut Tollu: Necmettin Erbakan University

77. Duygu Donmez Demir: Celal Bayar University

78. Duygu Yilmaz Eroglu: Uludag University

79. Ebru Ozbilge: Izmir University of Economics

80. Ekber Girgin: Sakarya University

81. Ekrem Savas: Istanbul Ticaret University

82. Elif Aydın: Ondokuz Mayıs University

83. Elif Cetin: Uludag University, Celal Bayar University

84. Elif Ercelik: Gebze Institute of Technology, Istanbul Technical University

85. Elvan Akın: Missouri University Science Technology

86. Emine Mısırlı: Ege University

87. Emrah Kılıc: TOBB University of Economics and Technology

88. Emrah Yılmaz: Firat University

89. Emre Deniz: Kirikkale University

90. Emrullah Yasar: Uludag University

91. Erbil Cetin: Ege University

92. Erdal Karapinar: Atilim University

93. Erdem Toksoy: Ondokuz Mayıs University


94. Erhan Koca: Celal Bayar University

95. Ertan Ibikli: Ankara University

96. Esen Iyigun: Uludag University

97. Esra Kamber: Sakarya University

98. Esra Karatas: Canakkale Onsekiz Mart University

99. Eylem Guzel Karpuz: Karamanoglu Mehmetbey University

100. F.Aliouane: University of Jijel

101. F.Mahmoudi: Universidad de Chile

102. Farrukh Mukhamedov: International Islamic University Malaysia

103. Fatih Kızılaslan: Gebze Institute of Technology

104. Fatma Calıskan: Istanbul University

105. Fatma Kanca: Kadir Has University

106. Fatma Karakoc: Ankara University

107. Fatma Ozen Erdogan: Uludag University

108. Fatma Serap Topal: Ege University

109. Fatma Tokmak: Gazi University and Ege University

110. Faycal Hamdi: RECITS Laboratory

111. Fırat Ates: Balikesir University

112. Figen Oke: Trakya University

113. Florian Munteanu: University of Craiova

114. Fuad Kittaneh: The University of Jordan & Jordan and Al-Ahliyya Amman University

115. Fulya Yoruk Deren: Ege University

116. Fumiaki Kohsaka: Oita University

117. Gabil Adilov: Akdeniz University

118. Georgy A. Omel’yanov: Universidad de Sonora

119. Gonca Durmaz: Kirikkale University

120. Gokhan Soydan: Uludag University

121. Guettal Djaouida: University Ferhat Abbas of Setif 1

122. Gurunath Rao Vaidya: Acharya Institute of Graduate Studies

123. Gulden Gun Polat: Istanbul Technical University

124. Gulden Kapusuz: Suleyman Demirel University

125. Gulnar Suleymanova: Kyrgyzstan-Turkey Manas University

126. Gulsah Yeni: Missouri University of Science and Technology

127. Gumrah Uysal: Karabuk University

128. Gulsum Ulusoy: Kirikkale University

129. H.Cenk Ozmutlu: Uludag University

130. H.M.Sadeghi: Eastern Mediterranean University

131. Hacer Sengul: Siirt University

132. Hakan Avcı: Ondokuz Mayıs University

133. Halis Aygun: Kocaeli University

134. Hamid Mottaghi Golshan: Islamic Azad University

135. Hamit Armagan: Suleyman Demirel University

136. Handan Engin Kırımlı: Uludag University

137. Harun Karsli: Abant Izzet Baysal University

138. Hasan Akın: Zirve University

139. Hasan Kose: Selcuk University

140. Hatice Yaldız: Duzce University


141. Hendra Gunawan: Institute of Technology Bandung

142. Hesna Kabadayı: Ankara University

143. Hideyuki Wada: Toho University

144. Hikmet Koyunbakan: Firat University

145. Huseyin Bereketoglu: Ankara University

146. Huseyin Ovalıoglu: Uludag University

147. Ibtissam Bouloukza: University of 20 August 1955

148. Ilknur Yesilce: Mersin University

149. Ismail U.Tiryaki: Abant Izzet Baysal University

150. Izhar Uddin: Aligarh Muslim University

151. I.Ilker Akca: Eskisehir Osmangazi University

152. Ibrahim Canak: Ege University

153. Ilhan Kucuk: Uludag University

154. Ilkay Yaslan Karaca: Ege University

155. Ilker Kucuk: Uludag University

156. Ilker Burak Giresunlu: Uludag University

157. Inci M.Erhan: Atılım University

158. Irem Baglan: Kocaeli University

159. Ishak Altun: Kirikkale University

160. Ismail Aydın: Sinop University

161. Ismail Naci Cangul: Uludag University

162. Ismet Karaca: Ege University

163. J.Davila: Universidad de Chile

164. J.Y.Kang: Hannam University

165. Jasbir S. Manhas: Sultan Qaboos University

166. K.Biroud: Universite Abou Bakr Belkaıd

167. Kadir Emir: Eskisehir Osmangazi University

168. Kadir Erturk: Namik Kemal University

169. Kathryn E.Hare: University of Waterloo

170. Kenan Tas: Cankaya University

171. Kubra Erdem Bicer: Celal Bayar University

172. Kyung Soo Kim: Kyungnam University

173. L.Kumar: Banaras Hindu University

174. Lashab Mohamed: Universite 20 Aout 1955-Skikda

175. Leili Kussainova: L.N. Gumilyov Eurasian National University

176. Luminita Grecu: University of Craiova

177. M.Emin Ozdemir: Ataturk University

178. M.Hariour: Badji Mokthtar-Annaba University

179. M.Imdad: Aligarh Muslim University

180. M.C.Bouras: Badji Mokthtar-Annaba University

181. M.S.Jusoh: Universiti Teknologi MARA

182. M.N.M.Fadzil: Universiti Teknologi MARA

183. M.S.M.Noorani: Universiti Kebangsaan Malaysia

184. Mahpeyker Ozturk: Sakarya University

185. Mansouri Khaled: Universite 20 Aout 1955-Skikda

186. Masashi Toyoda: Tamagawa University

187. Matallah Atika: Ecole preparatoire en sciences economiques


188. Meenu Goyal: Indian Institute of Technology Roorkee

189. Mehdi Asadi: Islamic Azad University

190. Mehmet Ali Ozarslan: Eastern Mediterranean University

191. Mehmet Emir Koksal: Mevlana University

192. Mehmet Yuksel: Cukurova University

193. Mehmet Zeki Sarıkaya: Duzce University

194. Merve Guney Duman: Sakarya University

195. Meryem Odabasi: Ege University

196. Meryem Oztop: Suleyman Demirel University

197. Mesliza Mohamed: Universiti Teknologi MARA

198. Messaoudene Hadia: University of Tebessa

199. Metin Basarır: Sakarya University

200. Mikail Et: Firat University

201. Mine Menekse: Gaziantep University

202. Mochammad Idris: Institute of Technology Bandung

203. Mohamed Amine Boutiche: Universite des sciences et de la Technologie Houari Boumediene

204. Mohamed Dalah: University of Constantine 1

205. Mohammed Derhab: University Abou-Bekr Belkaid Tlemcen

206. Mohamed Najib Ellouze: Sfax University

207. Mohammed Nehari: University Ibn Khaldoun Tiaret

208. Mourad Jelassi: Carthage University

209. Mourad Mordjaoui: University of 20 August 1955

210. Mourad Rahmani: USTHB

211. Moustafa El-Shahed: Qassim University

212. Muge Togan: Uludag University

213. Murteza Yılmaz: TOBB University of Economics & Technology

214. Musa Demirci: Uludag University

215. Mustafa Alkan: University of Akdeniz

216. Mustafa Inc: Firat University

217. Mustafa Kara: Eastern Mediterranean University

218. Mustafa Kazaz: Celal Bayar University

219. Mustafa Nadar: Istanbul Technical University

220. Mustafa Ozkan: Trakya University

221. Mustafa Topaksu: Cukurova University

222. Mustapha Yarou: Jijel University

223. Mutlay Dogan: Zirve University

224. N.Metiya: Bengal Institute of Technology

225. N.M.Badiger: Karnatak University

226. Nazim Idrisoglu Mahmudov: Eastern Mediterranean University

227. Nazli Yildiz Ikikardes: Balikesir University

228. Nazmiye Yilmaz: Selcuk University

229. Necati Taskara: Selcuk University

230. Neslihan Nesliye Pelen: Middle East Technical University

231. Nese Isler Acar: Mehmet Akif Ersoy University

232. Nese Omur: Kocaeli Universitesi

233. Nihal Yılmaz Ozgur: Balıkesir University

234. Nihal Tas: Balikesir University


235. Nihal Yokus: Karamanoglu Mehmetbey University

236. Nihat Akgunes: Necmettin Erbakan University

237. Nil Kucuk: Uludag University

238. Nilay Sager: Ondokuz Mayıs University

239. Nilgun G.Baydar: Suleyman Demirel University

240. Nouiri Brahim: University of Laghouat

241. Noor Halimatus Sa’diah Ismail: Universiti Teknologi MARA

242. Nuket Aykut Hamal: Ege University

243. Nurullah Yilmaz: Suleyman Demirel University

244. Nursel Ozturk: Uludag University

245. Ozan Demirozer: Suleyman Demirel University

246. Ozkan Coban: Suleyman Demirel University

247. Omer Akguller: Mugla Sıtkı Kocman University

248. Omer Kisi: Cumhuriyet University

249. Ozden Koruoglu: Balikesir University

250. Ozgur Ege: Celal Bayar University

251. Ozlem Acar: Kirikkale University

252. Ozlem Orhan: Istanbul Technical University

253. Oznur Kulak: Ondokuz Mayıs University

254. Oznur Oztunc: Balıkesir University

255. P.N.Agrawal: Indian Institute of Technology Roorkee

256. P.S.K.Reddy: S.I.T

257. R.Saian: Universiti Teknologi MARA

258. P.Shahi: Thapar University

259. Patricia J.Y.Wong: Nanyang Technological University

260. Rahal Mohamed: University Ferhat Abbas of Setif 1

261. Rahime Dere: University of Akdeniz

262. Rajai Alassar: King Fahd University of Petroleum & Minerals (KFUPM)

263. Ranjini P.S: Don Bosco Institute of Technology

264. Ravi Agarwal: Texas A&M University-Kingsville

265. Raziye Akbay: Suleyman Demirel University

266. Recep Sahin: Balikesir University

267. Redouane Drai: Welding and NDT Research Center (CSC)

268. Refik Keskin: Sakarya University

269. Reyhane Ercan: Suleyman Demirel University

270. Romulus Militaru: University of Craiova

271. Ruhan Zhao: State University of New York (SUNY)

272. Rustem Kaya: Eskisehir Osmangazi University

273. S.Kanas: University of Rzeszow

274. S.K.Upadhyay: Indian Institute of Technology

275. S.Madi: Badji Mokthtar-Annaba University

276. Said Grace: Cairo University

277. Salih Yalcinbas: Celal Bayar University

278. Safa Menkad: Hadj Lakhdar University

279. Safia Benmansour: Preparatory School of Economics of Tlemcen

280. Samet Erden: Bartın University

281. Sandeep Kumar: Acharya Institute of Technology


282. Sanjiv K.Gupta: Sultan Qaboos University

283. Sathish Kumar: Indian Institute of Technology Roorkee

284. Satish Iyengar: University of Pittsburgh

285. Sebahattin Ikikardes: Balikesir University

286. Seda Oguz: Cumhuriyet University

287. Seda Oral: Celal Bayar University

288. Seda Ozturk: Karadeniz Technical University

289. Sefa Anıl Sezer: Ege University

290. Selcuk Kayacan: Istanbul Technical University

291. Selma Altundag: Sakarya University

292. Selma Gulyaz: Cumhuriyet University

293. Sertac Erman: Kocaeli University

294. Servet Kutukcu: Ondokuz Mayıs University

295. Seval Ene: Uludag University

296. Seyda Ildan: Selcuk University

297. Sibel Koparal: Kocaeli University

298. Sibel Pasalı Atmaca: Mugla Sıtkı Kocman University

299. Sinem Sahiner: Izmir University

300. Sinem Unul: Eastern Mediterranean University

301. Smail Kelaiaia: University of Annaba

302. Snezhana Hristova: Plovdiv University

303. Sonia Degeratu: University of Craiova

304. Soumia Kharfouchi: Universite 3 Constantine

305. Suleyman Ciftci: Uludag University

306. Sumeyra Ucar: Balıkesir University

307. Sumeyye Bakım: KTO Karatay University

308. Senol Eren: Ondokuz Mayıs University

309. Serife Muge Ege: Ege University

310. Sukran Konca: Sakarya University, Bitlis Eren University

311. T.Som: Banaras Hindu University

312. Tacksun Jung: Kunsan National University

313. Tahia Zerizer: Jazan University

314. Temel Ermis: Eskisehir Osmangazi University

315. Teoman Ozer: Istanbul Technical University

316. Tevfik Sahin: Amasya University

317. Tuba Vedi: Eastern Mediterranean University

318. Tuba Yigit: Suleyman Demirel University

319. Tugba Senlik: Ege University

320. Tuncay Yigit: Suleyman Demirel University

321. Tuncer Acar: Kirikkale University

322. U.K.Misra: Berhampur University

323. Ugur Yuksel: Atilim University

324. Ummahan Akcan: Anadolu University

325. Usha A.: Alliance University

326. Umit Sarp: Balikesir University

327. Umit Totur: Adnan Menderes University

328. Ummugulsum Ogut: Sakarya University


329. V.Lokesha: Vijayanagara Sri Krishnadevaraya University

330. Valery Gaiko: National Academy of Sciences of Belarus

331. Veli Kurt: University of Akdeniz

332. Vildan Cetkin: Kocaeli University

333. Vishwanath P.Singh: Karnatak University

334. Vladimir V.Kruchinin: Tomsk State University of Control Systems and Radioelectronics

335. Wan Zheng-su: Hunan Institute of Science and Technology

336. Yasemin Cengellenmis: Trakya University

337. Yasin Yazlik: Nevsehir Haci Bektas Veli University

338. Yasunori Kimura: Toho University

339. Yasar Bolat: Kastamonu University

340. Yavuz Selim Balkan: Duzce University

341. Yilmaz Simsek: University of Akdeniz

342. Young-Ho Kim: Changwon National University

343. Zdzislaw Rychlik: Maria Curie-Sk lodowska University

344. Zehra Sarıgedik: Celal Bayar University

345. Zennir Khaled: University 20 Aout 1955

346. Zerrin Onder: Ege University

347. Zhang Xiao-yong: Shanghai Maritime University

Date post:	11-Jan-2017
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International Congress in Honour of Professor Ravi P. Agarwal

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