+ All Categories
Home > Documents > 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th...

12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th...

Date post: 08-Jan-2020
Category:
Upload: others
View: 3 times
Download: 0 times
Share this document with a friend
42
12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview Function Centre Newcastle, NSW, Australia Book of Abstracts
Transcript
Page 1: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

 

12thInternationalConferenceonFixedPointTheoryandItsApplications

24–28July,2017

HarbourviewFunctionCentre

Newcastle,NSW,Australia

BookofAbstracts

 

Page 2: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview
Page 3: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

Book of Abstracts12th International Conference on Fixed Point Theory and Its Applications

24–28 July, 2017

Harbourview Function CentreNewcastle, NSW, Australia

Contact:[email protected]

Dedicated to the memory of Jonathan M. Borwein (* 20 May 1951,† 2 August 2016) in recognition of his prodigious contributions tononlinear analysis.

Jon M. Borwein(1951–2016)

Celebrating William (Art) Kirk’s

William (Art) Kirk

80th birthday and the 70th birthday of Brailey Sims.

Brailey Sims

The purpose of the conference is to bring together leading expertsand researchers in fixed point theory and to assess new develop-ments, ideas and methods in this important and dynamic field.A special emphasis will be put on applications in related areas,as well as other sciences, such as the natural sciences, medicine,economics and engineering.

Page 4: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 4

1 Important locations

Map provided by Google.

Conference Venue Harbourview Function Centre, 150 Wharf Rd,Newcastle NSW 2300, Australia

Welcome Reception Venue Customs House Hotel, 1 Bond St, Newcas-tle NSW 2300, Australia

Dinner Venue Quality Hotel NOAH’S On The Beach, ShortlandEsplanade & Zaara St, Newcastle East NSW 2300, Australia

Page 5: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 5

2 Welcome

Welcome to ICFPTA2017—the 12th International Conference onFixed Point Theory and Its Applications. The organisers wouldparticularly like to welcome participants who have travelled a longway to be here. We hope many of you will be able to take the op-portunity to have a look around Newcastle, and perhaps furtherafield, during your visit to Australia—there is much to see.

This conference follows the usual format of the ICFPTA series,which is to solicit contributions for the proceedings after the con-ference has concluded. These will be subjected to standard peerreview and those accepted will appear in a special issue of the Jour-nal of Nonlinear and Convex Analysis.

The conference continues the tradition of the previous fixedpoint theory meetings which were held in Marseille (1989), Halifax(1991), Seville (1995), Kazimierz Dolny (1997), Haifa (2001), Valencia(2003), Guanajuato (2005), Chiang Mai (2007), Changhua (2009),Cluj-Napoca (2012) and Istanbul (2015).

Special thanks are due to Juliane Turner and David Allinghamfor the extensive administrative and technical support they haveprovided throughout the organisation of ICFPTA2017. We mustalso mention the conference sponsors listed on page 6, withouttheir support the conference could not have run.

Brailey Sims, chair of the organising committee

3 Organising committee

Brailey Sims (Chair)

Björn Rüffer

George Willis

Erdal Karapinar

Aidan Sims

Helga Fetter

Juliane Turner

David Allingham

Page 6: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 6

4 Sponsors

Senior Deputy Vice-Chancellor (Research & Innovation), Universityof Newcastle, Australia

CARMA (Priority Research Centre for Computer-Assisted ResearchMathematics And its applications, University of Newcastle, Aus-tralia)

School of Mathematical and Physical Sciences, University of New-castle, Australia

Australian Mathematical Socienty

5 Scientific committee

Shigeo Akashi (Japan)

Aksoy Asuman (USA)

Vasile Berinde (Romania)

Yunan Cui (P. R. China)

Sompong Dhompongsa (Thai-land)

Tomas Dominguez Benavides(Spain)

Jesus Garcia Falset (Spain)

Helga Fetter (Mexico)

Marlene Frigon (Canada)

Berta Gamboa de Buen (Mexico)

Kazimierz Goebel (Poland)

Maria de Los Angeles JaponPineda (Spain)

Mikio Kato (Japan)

Erdal Karapinar (Turkey)

Jong Kyu Kim (South Korea)

William (Art) Kirk (USA)

Ulrich Kohlenbach (Germany)

Anthony To-Ming Lau (Canada)

Christopher Lennard (USA)

Lai-Jiu Lin (Taiwan)

Enrique Llorens Fuster (Spain)

Genaro Lopez Acedo (Spain)

Elisabetta Maluta (Italy)

Giuseppe Marino (Italy)

Sehie Park (South Korea)

Adrian Petrusel (Romania)

Somyot Plubtieng (Thailand)

Simeon Reich (Israel)

Biagio Ricceri (Italy)

Naseer Shahzad (Saudi Arabia)

Brailey Sims (Australia)

Suthep Suantai (Thailand)

Tomonari Suzuki (Japan)

Wataru Takahashi (Japan)

Mansur Vaezpour (Iran)

Hong-Kun Xu (P. R. China)

6 Invited speakers

Chris Lennard, University of Pittsburgh

Hong-Kun Xu, Hangzhou Dianzi University

Stanislaw Prus, M. Curie-Sklodowska University

Tomas Benavides, University of Seville

Page 7: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 7

7 Housekeeping

7.1 Welcome reception

A welcome reception will be held from 4pm–6pm at CustomsHouse Hotel, 1 Bond St, Newcastle NSW 2300, Australia.

7.2 Registration desk

Each delegate is required to register upon arrival at the conference.You will be able to register on Monday 24 July from 8.30am in theconference venue.

Upon registration, delegates will receive a name badge, satcheland final program.

7.3 Transport

Getting to Newcastle is easy and the city is the hub of the HunterValley, one of Australia’s most attractive holiday and tourism des-tinations. Newcastle is only 2 hours north of Sydney and has road,rail, sea and air access.

7.4 Taxi

If you need to call a Taxi, you can call 13 33 00.

7.5 Contact number whilst at the conference

If you would like to be contacted whilst attending the conference acall can be made to Juliane Turner on +61 (0) 429188504.

7.6 Conference dinner

This dinner will be held at Noah’s On The Beach, Corner ShortlandEsplanade & Zaara St, Newcastle East on Thursday at 6:30pm.

Special dietary requirements If you have any dietary requirementsplease confirm them at the registration desk.

7.7 Internet access

Internet access is available to delegates. Please see the RegistrationDesk for details.

7.8 Eating, tours & things to do

Restaurants nearby All within walking distance of the conferencevenue.

Honeysuckle, where many eateries and bars are to be found withstunning harbour views.

Page 8: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 8

The Queen’s Wharf Hotel, again with excellent harbour views, isright next door.

Estabar Shop 1, 61 Shortland Esplanade, Newcastle. Ph: 4927 1222.Open for breakfast and lunch every day. Estabar’s does sensa-tional yoghurt-pistachio-nut-honey parfait’s, the usual range ofbreakfast foods, and a wonderful Spanish hot chocolate. Greatcoffee, excellent gelato and milkshakes. The seated bar area looksout over the water at Newcastle Beach.

Scotties 36 Scott Street, Newcastle. Ph: 4926 3780. Open Wednesday–Saturday, 7am til late, Sunday, 7am 7pm. Closed Monday andTuesday. Interesting meal options such as smoked salmon withIndian spices. Recommended for dinners.

Moor Newcastle East brings to you an eclectic fare with fresh andaromatic flavours stemming fromÂaMiddle Eastern, Spanish andNorth African influences.

Sandbar at Newcastle Beach Shortland Esplanade, Newcastle. Ph:4927 8668. Open Wed–Fri lunch and dinner, Saturday all day andSunday breakfast and lunch. Good variety of a-la-carte food andmeal size options. Fully licensed. Also, a nice place for a drinkon the Beach Terrace.

Liquid Gold Beach Cafe with great views award winning baristahome style cooking shop 102 -61 Shortland esplanade, Newcas-tle, New South Wales 2300

Pacific and Hunter Street There is also a large range of cafés andrestaurants on Pacific and Hunter Street including ElementsCafé, Soul Café, Sprocket Roasters, Paymasters Café, The GrainStore (with an interesting beer selection on tab).

Things to do in Newcastle The following is a list of local points ofinterest, all within walking distance of the conference venue.

Walk the Bathers Way, a 5km coastal walk from Nobbys Light Houseto Merewether.

Newcastle East Heritage Walk, an about 3km walk (1 12 –2 hour com-

fortable walk). Points of interest include; Nobby’s Headland,Fort Scratchley, Ocean Bathes, Obelisk, Christ Church Cathedral,Stationmasters Residence

Bogey Hole at Newcastle Beach, a hand-hewn ocean rock pool carvedout of a cliff face by convicts in the 19th century.

Fort Scratchley. Only fort in Australia to fire on the enemy (WW2)

http://www.fortscratchley.com.au/

The Lock Up. 1800’s Police Station and Contemporary Art Centre

http://www.thelockup.org.au/

Page 9: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 9

Newcastle Musem. Open 7 days during NSW school holidays andPublic Holidays. Free admission for general exhibitions.

http://www.newcastlemuseum.com.au/

Newcastle Maritime Centre. Explore the rich maritime history ofNewcastle and the Hunter River, and learn about the port’s im-portance to the development of Australia from the early days ofEuropean settlement to the present time. Entry: $10/adult and$5/child.

https://mgnsw.org.au/organisations/newcastle-maritime-centre/

A short ferry ride to Stockton and the General Washington Hotel. Ferryservice between Stockton Wharf and Newcastle Wharf daily from5am until 11pm (10pm Sundays), every half hour for most ofthe day. The ferry trip from Stockton Wharf to Newcastle Wharftakes approximately five minutes.

https://transportnsw.info/

http://www.newcastlebuses.info/

The General Washington Hotel in Stockton (short walk from theferry) is known for good beer, food and especially sea food.

The following are some popular tourist places of interest a shortdrive away (within 15km of the conference venue).

Blackbutt Reserve. See a variety of bird species plus koalas, kanga-roos and wombats at Blackbutt Reserve. Open 9am–5pm everyday. Free entry. Carnley Avenue, Kotara.

http://www.newcastle.nsw.gov.au/recreation/blackbutt_reserve

Hunter Wetlands Centre, where you can explore the network ofponds in a canoe. 412 Sandgate Road, Shortland. Ph: 4951

6466. Open Mon–Fri 9am–4pm and weekends 9am–5pm. En-try $5/person.

http://www.wetlands.org.au/page4627/Home.aspx

Darby Street, in Cooks Hill, a bohemian strip with eclectic bou-tiques, bookshops and cafés. A great place to wander duringthe day with lots of great cafes for morning/afternoon tea andlunch.

Beaumont Street, Hamilton, Home to Newcastle’s first Italian andGreek arrivals, there is a strong Mediterranean focus with manysidewalk cafes and a thriving pub-scene. Multicultural eat street,with some 46 restaurants ranging from casual to formal dining.

Honeysuckle, Working wharves are becoming places of play withthe creation of foreshore promenades and open squares offeringwaterfront cafes and restaurants - all with glorious views.

Page 10: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 10

8 Abstracts of the contributed talks

8.1 Monday 24 July 2017

Plenary: “Characterizing geometric and topological properties ofsets and spaces via fixed point properties”by Chris Lennard

9:00am — Harbourview Room

MORNING TEA — 10:30am

“On the Banas-Hajnosz-Wedrychowicz type Modulus of Convex-ity and Fixed Point Property”by Ji Gao, Satit Saejung

Abstract. Let X be a Banach space, and B(X) and S(X) be theunit ball and unit sphere of X. In this talk, inspired by Banas etal., the new parameterSYX(ε) = sup{〈x− y, fx〉 : x, y ∈ S(X), ||x + y||/2 ≥ 1− ε} forsome fx ∈ ∇x, where ∇x ⊂ S(X∗) is the norm 1 supportingfunctional at x, is introduced. Several properties of thisparameter are investigated. The main result are that ifSYX(t) < 2, for some t ∈ (0, 1] then X is uniformly non-square;and if SYX(ε) < 1 + 2ε, for some ε ∈ (0, 1/2) then both X andX∗ have uniform normal structure.In particular, if εU = limε→0 SYX(ε) < 1, then X is uniformlynon-square and both X and X∗ have uniform normal structure.We have an example to show this condition is the best possible.

11:00am — Harbourview Room

Page 11: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 11

“Common fixed point theorems for set-valued fuzzy weakly con-tractive mappings in complete metric spaces”by Iram Iqbal, Nazra Sultana, Ambreen Fatima

Abstract. To solve complicated problems in economics,engineering, and environment, we cannot successfully useclassical methods because of various uncertainties for thoseproblems. The most appropriate theory, for dealing withuncertainties is the theory of fuzzy sets. In present paper, wedetermine common fixed point theorems for a pair of set-valuedfuzzy mappings under a weakly contractive condition viaα∗-admissibility with respect to a function η. As an application,we prove common fixed point results for fuzzy mappings inmetric linear space with d∞-metric (induced by Hausdorffmetric). The results obtained here, generalize some existingresults in the literature and are illustrated with examples.

11:00am — Hunter Room

“Lim’s Center and Fixed Point Theorems for Isometry Mappings”by S. Rajesh, P. Veeramani

Abstract. In this paper, we prove that if K is a nonempty weaklycompact convex set %having normal in a Banach space such thatK has the hereditary fixed point property and F is a commutingfamily of isometry mappings on K, then there exists a point inC(K) which is fixed by every member in F whenever C(K) is acompact set. Also, we give an example to show that C(K), theset of Chebyshev center of K, need not be invariant underisometry maps. This example answers the question: "Is theChebyshev center invariant under isometry maps?" raised byLim et al. Further, we give a simple example to illustrate thatthe Lim’s center, introduced by Lim, is different from theChebyshev center.

11:30am — Harbourview Room

Page 12: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 12

“On new fixed point results via a generalize extended simulationfunction in b-metric spaces”by Oratai Yamaod, Wutiphol Sintunavarat

Abstract. In this work, we guarantee the existence of fixed pointfor new nonlinear mappings by using the new concept of anes-simulation function in b-metric spaces. The main resultimproves and generalizes the result of Hierro and Samet (J.Fixed Point Theory Appl. (2016).doi:10.1007/s11784-016-0385-x). We also provide an example toillustrate the results presented herein.

11:30am — Hunter Room

LUNCH — 12:00pm

“Characterization of weak compactness through fixed point exis-tence theorems”by Maria Japon

Abstract. P.K.Lin and Y.Sternfeld proved the followingcharacterization of norm-compactness:

Let L > 1. A closed convex subset C of a Banach space isnorm-compact if and only if every L-Lipschitzian mapping T : C → Chas a fixed point.

As a consequence of results given by F. Browder and W. Ray, thefollowing statement also holds:

Let H be a Hilbert space. A closed convex subset C ⊂ H is weaklycompact if and only if every nonexpansive mapping T : C → C has afixed point.

It is well-known that fixed point property for nonexpansivemappings does not generalize weak compactness in general: K.Goebel and T. Kuczumow constructed a family of closed convexand not weakly compact subsets of `1 with the fixed pointproperty for such mappings.

In this talk we will check that if the definition ofnonexpansiveness is slightly modified, weak compactness canstill be characterized by fixed point theorems in a wide class ofBanach spaces.

1:30pm — Harbourview Room

Page 13: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 13

“The fpp and the AFPP in a family of spaces in which c0 hasfinite codimension”by Helga Andrea Fetter Nathansky, Jeimer Villada Bedoya

Abstract. In this talk we give an example of an equivalentrenorming of c0 in which the sets with the f pp are the same asthose of c0 but the families of sets with the AFPP are different.In order to achieve this, we give some results about therelationship of non w− compact sets and the f pp in a specialfamily of spaces in which c0 has finite codimension.

2:00pm — Harbourview Room

“Reflexivity is equivalent to stability of the AFPP”by Jeimer Villada, Helga Fetter, Maria Japon

Abstract. In this work we show that the family of closed convexsets with the almost fixed point property is not stable underrenormings for non-reflexive Banach spaces. This together witha result by Reich, shows that a Banach spaces is reflexive if andonly if it has the same family of closed convex sets with thealmost fixed point property for every equivalent norm.

2:30pm — Harbourview Room

AFTERNOON TEA — 3:00pm

“The stable weak∗ fixed point property in `1”by Łukasz Piasecki, Emanuele Casini, Enrico Miglierina, RoxanaPopescu

Abstract. We give a characterization of the preduals of `1 suchthat `1 has the stable weak∗ fixed point property fornonexpansive mappings.

3:30pm — Harbourview Room

Page 14: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 14

“Geometrical Properties that imply property S or property Sm”by Francisco Eduardo Castillo Santos

Abstract. In 2001 A. Wisnicki introduced properties S and Sm.In that article the author showed that if X is a Banach space andthere exists a free ultrafilter U on N such that the ultrapowerXU has property Sm, then the space X enjoys the fixed pointproperty. In this talk we show a wider class of spaces that enjoyseither property S or property Sm.We show how some of the usual concepts in fixed point theoryare closely related to Property S and Property Sm.

4:00pm — Harbourview Room

Finish — 4:30pm

Page 15: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 15

8.2 Tuesday 25 July 2017

Plenary: “Fixed Point Methods for Big Data Optimization Prob-lems”by Hong-Kun Xu

9:00am — Harbourview Room

MORNING TEA — 10:00am

“Applications of Tarski Fixed Point Theorem to Analysis on Sys-temic Risk in Dynamic Economic Systems”by Qingmin Hao, Jinlu Li

Abstract. Since Tariski proved the first fixed point theorem onlattices, fixed point theory on partially ordered sets has beenrapidly developed and it has been widely applied to manydifferent fields, such as, equilibrium problems with incompleteutilities; ordered variational inequalities; differential andintegral equation, etc. In this paper, we study the Eisenberg andNoe interbank model [1] that is extended from a static to adynamic contagious model with infinitely many periods. Theindustrial market is added into their economic systems. Weapply Tarski’s fixed point theorem on a chain-complete lattice toprove the existence of an iterative sequence of clearing paymentvectors period by period. The results show that, on the set ofclearing payment vectors at each period t > 0, after takesaccount of the interests of liabilities based on the differentperiods, the status of default or surplus for any node is stable;the values of profits of nodes with a surplus are constants; andthe value of the general debilities for a suffer node is thevariable. Based on the new clearing payment, we analyze thefeatures of different systemic risks with the related controllingresults.

10:30am — Harbourview Room

Page 16: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 16

“Attractive point theorems and convergence theorems for nonlin-ear mappings in Hilbert spaces”by Sachiko Atsushiba

Abstract. In this talk, we prove attractive points theorems fornonlinear mappings. We also study Halpern’s type iterationsand Mann’s type iterations for the nonlinear mappings. Further,we prove weak and strong convergence theorems by using theideas of fixed points, attractive points and acute points.

10:30am — Hunter Room

Page 17: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 17

“Existence of solutions of various mathematical problemsthrough fixed point theorems”by Deepak Singh

Abstract. The main purpose of this presentation is to highlightthe ascendancy of fixed point theory and its applications. Inmodern era, fixed point theory is employed in many areas ofmathematics and engineering. Keeping these utilizations offixed point theory in mind, some fixed point results are provedin the structure of partial b-metric spaces and allied abstractspaces which emphasize primarily the applications for existenceof the solution of various functional equations occurring indynamic programming, integral equations, boundary valueproblems, equations representing LCR circuits and simpleharmonic motion etc.(see in [1],[2],[3]). Moreover someinnovative examples are also offered which authenticate thevalidity of obtained results.Key words: Fixed point, partial b-metric spaces, b- metricspaces, integral equation, boundary value problem, dynamicprogramming.References:1. Pathaithep Kumrod , Wutiphol Sintunavarat, A newcontractive condition approach to Φ-fixed point results in metricspaces and its applications, Journal of Computational andApplied Mathematics, Volume 311, February 2017, Pages194-204.2. Wenying Feng and Guang Zhang, New fixed point theoremson order intervals and their applications, Fixed Point Theoryand Applications,2015, 2015:218.3. Angel Almeida, Antonio-Francisco Roldán-López-de-hierroand Kishin Sadarangani, On a fixed point theorem and itsapplication in dynamic programming, Applicable Analysis andDiscrete Mathematics, vol. 9, no. 2 (October 2015), pp. 221-244.

11:00am — Harbourview Room

Page 18: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 18

“Approximation of a common fixed point of two nonlinear map-pings with nonsummable errors in a Banach space”by Shunsuke Kajiba, Takanori Ibaraki, Yasunori Kimura

Abstract. In this talk, we study an iterative scheme for twononlinear mappings with errors in a uniformly convex anduniformly smooth Banach space. We consider that the sequenceincluding errors for obtaining the value of metric projection stillhas a nice property for approximating a common fixed point oftwo mappings. Moreover, we prove a convergence theorem for acommon fixed point of two mappings in a Banach space.

11:00am — Hunter Room

“Fixed point tools of Krasnosel’skii type for implicit integralequations ”by Dariusz Wardowski

Abstract. During the talk there will be taken into considerationthe integral equation in an implicit form which can betransformed to the equation with a sum of the compactmapping and the operator with a general contractive nature.Using the Hausdorff measure of noncompactness and thecondensing operators there will be presented a fixed pointtheorem of Krasnosel’skii type guaranteeing the existence of thepositive solution of the mentioned equation.

11:30am — Harbourview Room

Page 19: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 19

“New iterative method for the class of quasi-contractive operatorsand comparison of rate of convergence ”by Wutiphol Sintunavarat, Adoon Pansuwan

Abstract. The purpose of this talk is to propose a new iterativealgorithm to approximate fixed points of quasi-contractiveoperators introduced by Berinde [V.Berinde, A convergencetheorem for some mean value fixed point iterations procedures,Demonstratio Mathematica, 38 (2005) 177-184]. Also, someconvergence theorems with the purposed iterative algorithm inconvex metric spaces are established. A numerical example isalso given to examine the fastness of the proposed iterativealgorithm under different control conditions and initial pointswith the several iterative algorithm in the literatures.

11:30am — Hunter Room

“Fixed Point Theorems on Partially Ordered Banach Spaces andTheir Applications”by Jinlu Li

Abstract. In this paper, we study the connections between thenormality, the regularity, the fully regularity and thechain-complete property in partially ordered Banach spaces.Then by applying these properties, we prove some fixed pointtheorems on partially ordered Banach spaces. As applications ofthese fixed point theorems, we prove the existence of solutionsof some integral equations, such as Hammerstein integralequations, integral equations in Banach spaces.

12:00pm — Harbourview Room

“Convergence rates of the proximal point algorithm”by Shin-ya Matsushita

Abstract. In this talk, we investigate the convergence rate of theproximal point algorithm for finding a minimizer of properlower semicontinuous convex functions.

12:00pm — Hunter Room

LUNCH — 12:30pm

Page 20: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 20

“A new Φ-generalized quasi metric space with some fixed pointresults and applications”by Bahru Tsegaye Leyew, Mujahid Abbas and Safeer Hussain Khan

Abstract. The concept of a new Φ-generalized quasi metricspace is introduced. A number of well known quasi metricspaces are retrieved from Φ-generalized quasi metric space.Some general fixed point theorems in a Φ-generalized quasimetric spaces are proved, which generalize, modify and unifysome existing fixed point theorems in the literature. We alsogive applications of our results to obtain fixed points forcontraction mappings in the domain of words and to prove theexistence of periodic solutions of delay differential equations.

2:00pm — Harbourview Room

“A new class of fuzzy contractive mappings and fixed point theo-rems”by Dhananjay Gopal

Abstract. In this talk, we propose a new class of fuzzycontractive mappings which enlarge and unifies various knownclasses of fuzzy contractive mappings. For this new class ofmappings, suitable conditions are framed to ensure theexistence of fixed point in M-complete fuzzy metric spaces (inthe sense of George and Veeramani). A comprehensive set ofexamples are presented to support of claim.

2:00pm — Hunter Room

“On a classification of Lipschitz mappings”by Kazimierz Goebel, Kazimierz Goebel and Łukasz Piasecki

Abstract. We present here the short history and present state ofresearch on the notion of mean Lipschitz mappings. We takeinto account that most of the people involved in the theory arepresent in the CARMA meeting. We hope that the subject mayfind some followers among newcomers to the theory.

2:30pm — Harbourview Room

Page 21: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 21

“Lipschitzian mappings under renormings”by Victor Perez Garcia, Carlos A. Hernández-Linares, Juan R.Acosta-Portilla

Abstract. It is presented a characterization of lipschitzianmappings, which are invariant under any renorming. It isproved that under assumption of boundedness of domain, thiscollection of mappings are just certain nonexpansive affinemappings. We also compare the families of nonexpansivemappings under two equivalent norms.

3:00pm — Harbourview Room

AFTERNOON TEA — 3:30pm

“Coincidence point theorems for multivalued weak contractionsin modular metric spaces endowed with a graph”by Nazra Sultana, Iram Iqbal, Komal

Abstract. In this paper, we introduce Reich type of multi-valuedG-contraction on a modular metric space endowed with adirected graph. We establish some coincidence point theoremsfor these contractions in the frame work of modular metricspace. The modular metric space is a natural generalization ofclassical modular over linear spaces. We give examples toillustrate the usability of obtained results. Coincidence pointtheorems for single valued mappings and coincidence pointtheorems in partial ordered modular metric spaces are obtainedhere as application of our results.

4:00pm — Harbourview Room

Page 22: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 22

“Invariant Distribution Function in a b-Metric Space”by Umar Yusuf Batsari, Poom Kumam, Sompong Dhompongsa

Abstract. No doubt, a lot of theoretical researches were done inthe area of fixed point theory, the major concern now is how toutilise the established results in solving real lifeproblems(applications). Our work in this paper was motivatedby applications of fixed point theory in Markov processes.Primarily, we established the existence of an invariantdistribution function(fixed point) and its stability in a b-metricspace. Also, we show how a proper definition of a metric canease lot of work in applications. Our result improve andcomplement some existing results in the literature.

4:00pm — Hunter Room

“Best proximity point theorems of generalized weakly contractionmappings in partially order metric spaces”by Aphinat Ninsri, Wutiphol Sintunavarat

Abstract. In this work, we define the new concept of ageneralized weakly contractive condition for nonlinear non-selfmappings and establish new best proximity point theorems forsuch mappings with three control functions in partially orderedmetric spaces. This results generalize the main results of Babuand Leta [V. R. G. Babu and B. K. Leta, Best proximity pointsand coupled best proximity points of (ψ− φ− θ)-almost weaklycontractive maps in partially ordered metric spaces, FactaUniversitatis (NIS), 32, 73-94 (2017)].

4:30pm — Harbourview Room

Page 23: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 23

“Fixed Point Results for Contraction maps with (CLR) Property ”by Afrah Abdou

Abstract. In this work, we introduce the (CLR)-property for thehybrid pairs of single-valued and multi-valued mappings andgive some coincidence and common fixed point theorems for thehybrid pairs of some contractive conditions. Also, we will givesome examples to illustrate the main results in this paper. Ourresults extend and improve some results given by some authors

4:30pm — Hunter Room

Finish — 5:00pm

Page 24: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 24

8.3 Wednesday 26 July 2017

“Proof Mining in Convex Optimization”by Ulrich Kohlenbach

Abstract. We apply the logic-based method of proof mining,which aims at the extraction of explicit effective data, tononeffective proofs in Convex Optimization. In particular, wereport on the recent extraction of a polynomial rate ofasymptotic regularity from Bauschke’s solution of the minimaldisplacement conjecture. We also give such a polynomial ratefor iterations of compositions of arbitrary firmly nonexpansivemappings which each are asymptotically regular treated byBauschke, Martín-Márquez, Moffat, Wang.

9:00am — Harbourview Room

“Multi-valued Contraction Principle and Applications”by Adrian Petrusel, Gabriela Petrusel

Abstract. The aim of this talk is to present an extended variantof the contraction principle for multi-valued operators. Moreprecisely, the classical result of Nadler (1969) is enhanced byother conclusions which seem to be relevant, both from atheoretical point of view and an applicative one. The concept ofstrict fixed point (also called stationary point or endpoint) willbe also taken under consideration.

9:30am — Harbourview Room

“Domains of accretive operators in Banach spaces”by Omar Muñiz-Pérez, Jesús Garcia-Falset, Simeon Reich

Abstract. Let D(A) be the domain of an m-accretive operator Aon a Banach space E. We provide sufficient conditions for theclosure of D(A) to be convex and for D(A) to coincide with Eitself. Several related results and pertinent examples are alsoincluded.

10:00am — Harbourview Room

MORNING TEA — 10:30am

TOUR

Page 25: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 25

8.4 Thursday 27 July 2017

Plenary: “Properties of direct sums of Banach spaces”by Stanislaw Prus

9:00am — Harbourview Room

MORNING TEA — 10:00am

“Linear extensions and my collaboration with a fixed point”by David Yost

Abstract. This talk will survey linear extension theorems inanalysis and their applications. In general extensions are notunique, so it is interesting to ask whether the set-valuedextension operator admits a linear selection. We begin withTietze’s extension theorem and the Hahn-Banach theorem,highlighting the role played by intersecting balls, whichconnects naturally with M-ideals in Banach spaces andC∗-algebras. Then we examine the existence of large families ofsubspaces admitting linear Hahn-Banach extension operators, induals of non-separable Asplund spaces; this topic was part ofjoint work with a permanent fixture of ICFPTA, Brailey Sims.

10:30am — Harbourview Room

Page 26: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 26

“Normal structure revisited”by Elisabetta Maluta

Abstract. The concept of normal structure for a set or for anormed space X appeared for the first time in the literature as aproperty suitable to guarantee existence of a common fixedpoint for all the surjective isometries of a convex weaklycompact subset of X onto itself. Later on it was used in thefundamental result by W.A.Kirk about existence of fixed pointsfor nonexpansive selfmappings of convex weakly compact setshaving normal structure. Then, in the last ten years, it turnedout that normal structure is useful also in the study, ininfinite-dimensional spaces, of the properties of constant width(CW, for short) sets, as well as in the study of some classes ofsets defined by properties shared also by CW sets, in particulardiametrically complete (DC) sets (i.e.sets such that adding anypoint to the set produces a set of larger diameter) and sets withconstant radius f rom the boundary (CR). CW sets are a (generallystrict) subset of DC sets which are in turn a subset of CR sets.Several results are known about these classes of sets innonreflexive spaces, in particular an example is available in c0 ofa CW set with empty interior. On the other side, in spaces withnormal structure, no CR set, hence no DC and no CW set, canhave empty interior; as a consequence, the class of DC sets andthat of CR sets coincide. In some reflexive Banach space lackingnormal structure, DC sets with empty interior have been built,and therefore it seems natural to ask whether normal structureis required in reflexive spaces where all DC sets have nonemptyinterior or in spaces where the classes of DC and of CR setscoincide. We answer in the affirmative the second question,while we have a partial negative result for the first one.

11:00am — Harbourview Room

Page 27: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 27

“An algebraic property of the boundaries of Banach spaces”by Clemente Zanco, V. P. Fonf

Abstract. Let (X, ‖ · ‖) be a Banach space. A subset B of the unitsphere SX∗ of X∗ is called a boundary o f X if for any x ∈ X thereexists f ∈ B with f (x) = ‖x‖. A subset H of the unit ball of X∗

is called r− norming ( f or X) if sup f∈H | f (x)| ≥ r‖x‖ for everyx ∈ X; H is called norming if it is r−norming for some r 0.Some connections between the concepts of boundary and ofnorming set of a Banach space and the linear structure areinvestigated. In particular we prove that, if X is a Banach spacewhich does not contain an isomorphic copy of c0, B ⊂ SX∗ is aboundary of X and H ⊂ B is a maximal linearly independentsubset of B, then H is norming.

11:30am — Harbourview Room

“Construction of common fixed points for monotone nonexpan-sive semigroups”by Walter Wojciech M Kozlowski

Abstract. We discuss existence of common fixed points formonotone nonexpansive semigroups of mappings acting inBanach spaces. We describe then an iterative process toconstruct such fixed points and prove its weak convergence to acommon fixed points. We also touch upon applications andexamples of monotone nonexpansive mappings and semigroupsof such mappings.

12:00pm — Harbourview Room

LUNCH — 12:30pm

Page 28: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 28

“Douglas-Rachford Method for Non-Convex Feasibility Prob-lems”by Scott Lindstrom, Jonathan M. Borwein, Bishnu Lamichhane,Brailey Sims, Matthew Skerritt, Anna Schneider

Abstract. The Douglas-Rachford method has been employedsuccessfully to solve a variety of non-convex feasibilityproblems. In particular, it shows surprising stability whenapplied to finding the intersections of hypersurfaces. We provelocal convergence in the generalization of a case prototypical ofthe phase retrieval problem. In so doing, we also discoverphenomena which may inhibit convergence. Finally we illustratean application to solving boundary valued ordinary differentialequations.This talk includes discoveries from three closely related works:1. With Brailey Sims, Matthew Skerritt. ”ComputingIntersections of Implicitly Specified Plane Curves.” To appear inJournal of Nonlinear and Convex Analysis.2. With Jonathan M. Borwein, Brailey Sims, Anna Schneider,Matthew Skerritt. ”Dynamics of the Douglas-Rachford Methodfor Ellipses and p-Spheres.” Submitted to Set Valued andVariational Analysis.3. With Bishnu Lamichhane and Brailey Sims. ”Application ofProjection Algorithms to Differential Equations: Boundary ValueProblems,” in preparation with plans to submit to ANZIAMJournal.

2:00pm — Harbourview Room

Page 29: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 29

“Regularizing with Bregman–Moreau envelopes”by Minh Dao, Heinz H. Bauschke, Scott B. Lindstrom

Abstract. Forty years ago, Attouch proposed to use the Moreauenvelope for regularization. Since then, this branch of convexanalysis has developed in many fruitful directions. In a differentdevelopment, in 1967, Bregman introduced what is nowadaysthe Bregman distance as a measure of discrepancy between twopoints generalizing the square of the Euclidean distance.Proximity operators based on the Bregman distance havebecome a topic of significant research as they are useful inalgorithmic solution of optimization problems. In this work, wecomplement these two different strands of convex analysis bysystematically investigating regularization aspects of theBregman–Moreau envelope. We also present various naturalextensions of classical results and illustrate them with examples.

2:30pm — Harbourview Room

“A Perron-Frobenius type result for integer maps”by Ohad Giladi, Björn S. Rüffer

Abstract. The Perron-Frobenius theory is concerned withstudying eigenvectors of positive maps. We discuss this theoryin the context of integer maps, and show that for certain mapson the d-dimensional lattice of positive integer points,’approximate’ eigenvectors can be found. Some applications ofthis result will also be discussed.

3:00pm — Harbourview Room

AFTERNOON TEA — 3:30pm

Page 30: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 30

“Parallel iterative methods for solving the split common nullpoint problems in Banach spaces”by Jong Kyu Kim

Abstract. In this talk, from the idea of Takahashi, we introduce anew parallel iterative method which based on the hybridprojection method for solving the split common null pointproblem of finding an element

x∗ ∈ S = ∩Ni=1 A−1

i 0∩ T−1(∩Mj=1B−1

j 0) 6= ∅,

where Ai and Bj are maximal monotone operators on theBanach spaces E1 and E2, respectively, and T : E1 → E2 is abounded linear operator. Some applications of the main resultfor the the problem of finding minimizers of convex functionsand the MSSFP in two Banach spaces are viewed. And also, wegive a numerical example to illustrate our main results andshowing its performance. Our results are the extensions of thecorresponding ones of Takahashi.Keywords: Split common null point problem, maximalmonotone operator, generakized resolvent.AMS 2010 Mathematics subject classification: 47H05, 47H09,49J53, 90C25.

4:00pm — Harbourview Room

“Fixed point theorems for nonexpansive self-maps on a boundedIsbell-convex quasi-pseudometric space”by Olivier Olela Otafudu, Hans-Peter Künzi

Abstract. In this talk, we present some fixed point theorems fornonexpansive self-maps on a bounded Isbell-convexquasi-pseudometric space. In analogy with a metric result, weshow among other things that a set-valued mapping T∗ on anIsbell-convex T0-quasimetric space (X, d) which takes values inthe space of nonempty externally Isbell-convex subset of (X, d)always has a single-valued selection T which satisfiesd(T(x), T(y)) ≤ dH(T∗(x), T∗(y)) whenever x, y ∈ X.(Here dH isthe usual extended Hausdorff quasi-pseudometric determinedby d on the set of nonempty subsets of X).

4:00pm — Hunter Room

Page 31: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 31

“Weakly Sharp Solutions of a Variational Inequality and its Con-vergence of Algorithms”by Yina Liu, Zili Wu, Jinsong Xu

Abstract. Weakly sharp solutions of variational inequalities areshown to be meaningful for nonlinear programming. Theirresults play a very important role in analyzing convergence ofalgorithms. However, most existing results are based on dualgap functions. There is little research characterizing weaklysharp solutions of variational inequalities by using primal orsome new gap functions. Since the primal gap function is easierto be calculated, the application of it will be much more fruitful.The aim of the paper is to characterize weakly sharp solutions ofa variational inequality problem. In particular, the primal anddual gap functions and their new combinations are used.Moreover, we also show this result without considering gapfunctions. Some finite convergence properties to the sequencesgenerated by the algorithms for solving variational inequalitiesare also included.

4:30pm — Harbourview Room

“Some fixed point theorems for Φ-maps in A-metric spaces”by Rohen Yumnam, Bulbul Khomdram

Abstract. In this note, we prove the existence and uniqueness offixed points for mappings satisfying Φ-maps in the setting ofA-metric spaces. Our results generalise various existing fixedpoint results in A-metric spaces.

4:30pm — Hunter Room

Finish — 5:00pm

Page 32: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 32

8.5 Friday 28 July 2017

Plenary: “Fixed points for affine mappings without compactnessassumptions”by Tomas Benavides

9:00am — Harbourview Room

MORNING TEA — 10:00am

“On convex combinations in geodesic spaces and extension ofmappings”by Rafael Espínola, Adriana Nicolae, Oscar Madiedo Castro

Abstract. In this talk we will consider the problem of how todeal with convex combinations in Busemann convex geodesicspaces. This subject has been studied in order to obtain KKMtheorems in geodesic spaces. We will describe two differentways to consider convex combinations in these spaces for afinite family of points and show some continuity properties onthe points and the coefficients. These continuity properties findan immediate application in the extension of continuous andLipschitz functions that, if time allows, will also be consideredin this talk.

10:30am — Harbourview Room

“‘Lion-Man’ and the Fixed Point Property”by Adriana Nicolae, Genaro López-Acedo, Bozena Piatek

Abstract. This talk focuses on the relation between the fixedpoint property for continuous mappings and a discrete lion andman game played in a strongly convex domain. Our main resultstates that in locally compact geodesic spaces, the compactnessof the domain is equivalent to its fixed point property, as well asto the success of the lion.

11:00am — Harbourview Room

Page 33: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 33

“Iterative schemes with errors for zero point problems in a Ba-nach space”by Takanori Ibaraki

Abstract. In this talk, we study an iterative scheme for twodifferent types of resolvents of a monotone operator defined ona Banach space. These resolvents are generalizations ofresolvents of a monotone operator in a Hilbert space. We obtainiterative approximations of a zero point of a monotone operatorgenerated by the shrinking projection method with errors in aBanach space. Using our result, we discuss some applications.

11:30am — Harbourview Room

“Metric fixed point theory: past, present and future — a personalperspective”by Brailey Sims

Abstract.

12:00pm — Harbourview Room

LUNCH — 12:30pm

Discussion — 1:30pm

Closing Ceremony — 2:30pm

Page 34: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 34

9 Abstracts of the plenary talks

The venue for all plenary lectures is the Harbourview Room.

“Characterizing geometric and topological properties of sets andspaces via fixed point properties”by Chris Lennard.

Abstract. A major theme in Fixed Point Theory is characterizinggeometric and topological properties of sets or spaces in termsof fixed point properties.From Brouwer (1912), Schauder (1930) and Klee (1955), we knowthat closed and convex subsets K of a Banach space X are normcompact if and only every continuous map on K has a fixedpoint.Also, Jaggi (1983) and Kassay (1986) proved that a reflexiveBanach space X has normal structure if and only if every Jagginonexpansive map on a closed bounded convex subset of X hasa fixed point. And Maurey (1980) and Dowling-L (1997) showedthat for a subspace X of (L1[0, 1], ‖ · ‖1), X is reflexive if andonly if every nonexpansive map on a closed bounded convexsubset of X has a fixed point.Moreover, by Maurey (1980) and Dowling-L-Turett (2004), aclosed bounded convex subset K of (c0, ‖ · ‖∞) is weaklycompact if and only if every nonexpansive map on K has a fixedpoint. And L-Nezir (2014), using a theorem of DomínguezBenavides (2009), proved that a Banach lattice (X, ‖ · ‖) isreflexive if and only if X has an equivalent norm ‖ · ‖∼ such thatevery ‖ · ‖∼-cascading nonexpansive map has fixed point.It is a fascinating open problem to discover a geometriccondition on equivalent norms ‖ · ‖ on (`1, ‖ · ‖1), characterizingwhen every ‖ · ‖-nonexpansive map on a closed boundedconvex subset has a fixed point.In this talk we will discuss recent developments in Fixed Pointand Banach Space Theory related to this circle of ideas.

Monday 9:00am

Page 35: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 35

“Fixed Point Methods for Big Data Optimization Problems”by Hong-Kun Xu.

Abstract. A big data optimization usually has an objectivefunction that is a sum of a large number of convex functionspossibly plus an additional simple convex function asregularization. In this talk we will discuss how fixed pointmethods can effectively be employed to solve a big dataoptimization. More precisely, we will present some fixed pointmethods (such as parallel and cyclic projection methods) forfirst-order methods in convex optimization and their Nesterovacceleration. For a big data problem on networks we will alsoaddress the issue of how fixed point methods work fordecentralized consensus solutions.

Tuesday 9:00am

“Properties of direct sums of Banach spaces”by Stanislaw Prus.

Abstract. One of research directions in geometry of Banachspaces is to study conditions under which geometric propertiesare preserved under passing to direct sums. We overviewselected results obtained in this direction and give someapplications of direct sums.In general direct sums have the form (∑i∈I Xi)E, where {Xi}i∈I

is a family of Banach spaces and the norm in the direct sumcomes from a Banach lattice E. The most desired result ongeometry of direct sums assures that the direct sum has a givengeometric property if all spaces Xi posses this property in theuniform way and E has an appropriate property. To define theuniformity we need to use a constant or a modulus associatedwith the considered geometric property. Many such constantsand moduli reflecting geometric properties of Banach spaces areused in the metric fixed point theory.We discuss results giving estimates of some constants andmoduli for a direct sum (∑i∈I Xi)E in terms of their values forthe spaces Xi. This includes James constant, Garcia-Falsetcoefficient and Opial modulus. In the case of a sum (X1 ⊕ X2)E

of two spaces, we discuss results assuring the weak fixed pointproperty in the direct sum under the assumption of the weakfixed point property in X1.

Thursday 9:00am

Page 36: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 36

“Fixed points for affine mappings without compactness assump-tions”by Tomas Benavides.

Abstract. In many Banach spaces, every nonexpansive mappingT defined from a convex closed bounded subset C into C has afixed point. However, in some other spaces this assertion isfalse. It can be surprising that, as observed in [1], most relevantexamples about the failure of the fixed point property fornonexpansive mappings in closed convex bounded sets involveaffine mappings. In this talk we will show that, in the case ofL1-like spaces and due to Komlos’ Theorem, the failure of thefixed point property for affine nonexpansive mappings can onlyoccur in a very restricted class of sets. We associate to anyclosed convex bounded subset C of X a coefficient t(C) ∈ [1, 2]which can be understood as a measure of the “non-closedness”of C for the topology of convergence in measure and we showsome fixed point results for affine Lipschitzian mappings,depending on the value of t(C), the value of the Lipschitzconstants of the iterates and the Opial modulus for the topologyof convergence in measure. Our result provides a widecollection of convex closed bounded sets in L1([0, 1]) and insome other spaces of functions, including the unit ball, whichsatisfy the fixed point property for affine nonexpansivemappings. Furthermore, this property is still preserved byrenorming when the Banach-Mazur distance is small enough(less than 2 in the case of the unit ball of L1(µ)). In particular,we prove that the failure of the fixed point property for affinenonexpansive mappings in L1(µ) can only occurs in theextremal case t(C) = 2. We will show some examples provingthat our fixed point stability results for nonexpansive mappingsare optimal in terms of the coefficient t(C).It is worth noting that, while standard fixed point results fornonexpansive mappings in L1(µ) assume compactness for theset C with respect to the topology of convergence in measure,due to our affinity assumption, we do not need anycompactness assumption for C.

[1] B. Sims, Examples of fixed point free mappings, Handbook ofMetric Fixed Point Theory, Kluwer academic Publishers, (2001),35–48.

Friday 9:00am

Page 37: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 37

10 List of participants

Adoon Pansuwan Thammasat University, [email protected]

Adrian Petrusel Babes-Bolyai University Cluj-Napoca, [email protected]

Adriana Nicolae University of Seville, [email protected]

Afra Abdou King Abdulaziz University, [email protected]

Anna Wardowska University of Lodz, [email protected]

Aphinat Ninsri Thammasat University, [email protected]

Bahru Tsegaye Leyew University of Pretoria, [email protected]

Björn Rüffer University of Newcastle, [email protected]

Brailey Sims University of Newcastle, [email protected]

Chris Lennard University of Pittsburgh, [email protected]

Clemente Zanco Università degli Studi di Milano, [email protected]

Dariusz Wardowski University of Lodz, [email protected]

David Yost Federation University, [email protected]

Deepak Singh National Institute of Technical Teachers Training and Research (NITTTR), [email protected]

Dhananjay Gopal S.V.National Institute of Technology, [email protected]

Elisabetta Maluta Politecnico di Milano, [email protected]

Francisco Eduardo Castillo Santos Universidad Juarez Autonoma de Tabasco, [email protected]

Gabriela Petrusel Babes-Bolyai University Cluj-Napoca, [email protected]

George Willis University of Newcastle, [email protected]

Helga Andrea Fetter Nathansky Centro de Investigación en Matemáticas, [email protected]

Hong-Kun Xu Hangzhou Dianzi University, [email protected]

Ian Searston [email protected]

Iram Iqbal University of Sargodha, [email protected]

Jeimer Alveiro Villada Bedoya Centro de Investigación en Matemáticas, [email protected]

Ji Gao Community College of Philadelphia, USA, [email protected]

Jinlu Li Shawnee State University, [email protected]

Jong Kyu Kim Kyungnam University, [email protected]

Kazimierz Goebel Maria Curie-Sklodowska University, [email protected]

Maria Angeles Japon Pineda Sevilla University, [email protected]

Minh Dao University of Newcastle, [email protected]

Nazra Sultana University of Sargodha, [email protected]

Ohad Giladi University of Newcastle, [email protected]

Olivier Olela Otafudu North-West University, [email protected]

Omar Muñiz-Pérez CONACYT - CIMAT, A.C. [email protected]

Oratai Yamaod Thammasat University, [email protected]

Qingmin Hao Tianjin University, [email protected]

Rajesh Sankara Narayanan Indian Institute of Technology Tirupati, [email protected]

Page 38: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 38

Rafael Espínola García Universidad de Sevilla, [email protected]

Sachiko Atsushiba University of Yamanashi, [email protected]

Samran Muntup Thummasat University, [email protected]

Scott Lindstrom University of Newcastle, [email protected]

Shin-ya Matsushita Akita Prefectural University, [email protected]

Shunsuke Kajiba Yokohama National University, [email protected]

Stanislaw Prus M. Curie-Sklodowska University, [email protected]

Takanori Ibaraki Yokohama National University, [email protected]

Tim Dalby [email protected]

Tomas Benavides University of Seville, [email protected]

Ulrich Kohlenbach TU Darmstadt, [email protected]

Umar Batsari Yusuf King Mongkut’s University of Technology Thonburi, [email protected]

Victor Perez Garcia Universidad Veracruzana, [email protected]

Walter (Wojciech M) Kozlowski UNSW, [email protected]

Wutiphol Sintunavarat Thammasat University, [email protected]

Yina Liu Xi’an Jiaotong-Liverpool University, [email protected]

Yumnam Rohen NIT MANIPUR, [email protected]

Łukasz Piasecki Uniwersytet Marii Curie-Skodowskiej, [email protected]

Page 39: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 39

11 Programme at a glance

Monday 24 July 2017

Harbourview Room Hunter Room

9:00am Chris Lennard (plenary)

10:30am morning tea

11:00am Ji Gao Iram Iqbal11:30am S. Rajesh Oratai Yamaod

12:00pm lunch

1:30pm Maria Japon2:00pm Helga Andrea Fetter

Nathansky2:30pm Jeimer Villada

3:00pm afternoon tea

3:30pm Łukasz Piasecki4:00pm Francisco Eduardo Castillo

Santos4:30pm (finish)

Tuesday 25 July 2017

Harbourview Room Hunter Room

9:00am Hong-Kun Xu (plenary)

10:00am morning tea

10:30am Qingmin Hao Sachiko Atsushiba11:00am Deepak Singh Shunsuke Kajiba11:30am Dariusz Wardowski Wutiphol Sintunavarat12:00pm Jinlu Li Shin-ya Matsushita

12:30pm lunch

2:00pm Bahru Tsegaye Leyew Dhananjay Gopal2:30pm Kazimierz Goebel3:00pm Victor Perez Garcia

3:30pm afternoon tea

4:00pm Nazra Sultana Umar Yusuf Batsari4:30pm Aphinat Ninsri Afrah Abdou5:00pm (finish)

Page 40: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 40

Wednesday 26 July 2017

Harbourview Room Hunter Room

9:00am Ulrich Kohlenbach9:30am Adrian Petrusel10:00am Omar Muñiz-Pérez

10:30am morning tea

TOUR

Thursday 27 July 2017

Harbourview Room Hunter Room

9:00am Stanislaw Prus (plenary)

10:00am morning tea

10:30am David Yost11:00am Elisabetta Maluta11:30am Clemente Zanco12:00pm Walter Wojciech M Kozlowski

12:30pm lunch

2:00pm Scott Lindstrom2:30pm Minh Dao3:00pm Ohad Giladi

3:30pm afternoon tea

4:00pm Jong Kyu Kim Olivier Olela Otafudu4:30pm Yina Liu Rohen Yumnam5:00pm (finish)

Friday 28 July 2017

Harbourview Room Hunter Room

9:00am Tomas Benavides (plenary)

10:00am morning tea

10:30am Rafael Espínola11:00am Adriana Nicolae11:30am Takanori Ibaraki12:00pm Brailey Sims

12:30pm lunch

1:30pm discussion2:30pm closing ceremony

Page 41: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

Index

Adrian Petrusel—Wednesday, 9:30am, 24

Adriana Nicolae—Friday, 11:00am, 32

Afrah Abdou—Tuesday, 4:30pm, 23

Aphinat Ninsri—Tuesday, 4:30pm, 22

Bahru Tsegaye Leyew—Tuesday, 2:00pm, 19

Brailey Sims—Friday, 12:00pm, 33

Chris Lennard—Monday, 9:00am, 34

Clemente Zanco—Thursday, 11:30am, 26

Dariusz Wardowski—Tuesday, 11:30am, 18

David Yost—Thursday, 10:30am, 25

Deepak Singh—Tuesday, 11:00am, 16

Dhananjay Gopal—Tuesday, 2:00pm, 20

Elisabetta Maluta—Thursday, 11:00am, 25

Francisco Eduardo Castillo Santos—Monday,4:00pm, 13

Helga Andrea Fetter Nathansky—Monday,2:00pm, 12

Hong-Kun Xu—Tuesday, 9:00am, 35

Iram Iqbal—Monday, 11:00am, 10

Jeimer Villada—Monday, 2:30pm, 13

Ji Gao—Monday, 11:00am, 10

Jinlu Li—Tuesday, 12:00pm, 19

Jong Kyu Kim—Thursday, 4:00pm, 29

Kazimierz Goebel—Tuesday, 2:30pm, 20

Maria Japon—Monday, 1:30pm, 12

Minh Dao—Thursday, 2:30pm, 28

Nazra Sultana—Tuesday, 4:00pm, 21

Ohad Giladi—Thursday, 3:00pm, 29

Olivier Olela Otafudu—Thursday, 4:00pm, 30

Omar Muñiz-Pérez—Wednesday, 10:00am, 24

Oratai Yamaod—Monday, 11:30am, 11

Qingmin Hao—Tuesday, 10:30am, 15

Rafael Espínola—Friday, 10:30am, 32

Rohen Yumnam—Thursday, 4:30pm, 31

S. Rajesh—Monday, 11:30am, 11

Sachiko Atsushiba—Tuesday, 10:30am, 15

Scott Lindstrom—Thursday, 2:00pm, 27

Shin-ya Matsushita—Tuesday, 12:00pm, 19

Shunsuke Kajiba—Tuesday, 11:00am, 17

Stanislaw Prus—Thursday, 9:00am, 35

Takanori Ibaraki—Friday, 11:30am, 32

Tomas Benavides—Friday, 9:00am, 36

Ulrich Kohlenbach—Wednesday, 9:00am, 24

Umar Yusuf Batsari—Tuesday, 4:00pm, 21

Victor Perez Garcia—Tuesday, 3:00pm, 20

Walter Wojciech M Kozlowski—Thursday,12:00pm, 27

Wutiphol Sintunavarat—Tuesday, 11:30am, 18

Yina Liu—Thursday, 4:30pm, 30

Łukasz Piasecki—Monday, 3:30pm, 13

Page 42: 12th InternationalConference Fixed Theory and Its Applications · Book of Abstracts 12th International Conference on Fixed Point Theory and Its Applications 24–28 July, 2017 Harbourview

book of abstracts 42

Contents

1 Important locations 4

2 Welcome 5

3 Organising committee 5

4 Sponsors 6

5 Scientific committee 6

6 Invited speakers 6

7 Housekeeping 7

7.1 Welcome reception 7

7.2 Registration desk 7

7.3 Transport 7

7.4 Taxi 7

7.5 Contact number whilst at the conference 7

7.6 Conference dinner 7

7.7 Internet access 7

7.8 Eating, tours & things to do 7

8 Abstracts of the contributed talks 10

8.1 Monday 24 July 2017 10

8.2 Tuesday 25 July 2017 15

8.3 Wednesday 26 July 2017 24

8.4 Thursday 27 July 2017 25

8.5 Friday 28 July 2017 32

9 Abstracts of the plenary talks 34

10 List of participants 37

11 Programme at a glance 39

Index 41


Recommended