scholarly journals Best Proximity Point Theorems for Cyclic Relatively ρ-Nonexpansive Mappings in Modular Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Karim Chaira ◽  
Samih Lazaiz
Keyword(s):  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Best Proximity Points ◽  
Admissible Sets ◽  
Modular Spaces

In this paper we introduce the notion of proximal ρ-normal structure of pair of ρ-admissible sets in modular spaces. We prove some results of best proximity points in this setting without recourse to Zorn’s lemma. We provide some examples to support our conclusions.

scholarly journals CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 4 ◽  
Author(s):  
Hassan Houmani ◽  
Teodor Turcanu
Keyword(s):  
Iterative Process ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Convergent Sequence ◽  
Best Proximity Points ◽  
New Class ◽  
Type Algorithm

We introduce a new class of non-self mappings by means of a condition which is called the (EP)-condition. This class includes proximal generalized nonexpansive mappings. It is shown that the existence of best proximity points for (EP)-mappings is equivalent to the existence of an approximate best proximity point sequence generated by a three-step iterative process. We also construct a CQ-type algorithm which generates a strongly convergent sequence to the best proximity point for a given (EP)-mapping.

scholarly journals Existence and Convergence Theorems of Best Proximity Points

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Banach Spaces ◽  
Convergence Theorem ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Best Proximity Points ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Relatively Nonexpansive

The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.

scholarly journals Proximal quasi-normal structure in convex metric spaces

2014 ◽  
Vol 22 (3) ◽  
pp. 45-58
Author(s):  
Moosa Gabeleh
Keyword(s):  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Best Proximity Points ◽  
New Class ◽  
Convex Metric Spaces

Abstract We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasi-normal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. Convex Anal. 14 (2013), 653-659].

scholarly journals A Best Proximity Point Result in Modular Spaces with the Fatou Property

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Modular Space ◽  
Fatou Property ◽  
Best Proximity Points ◽  
Modular Spaces

Consider a nonself-mapping , where is a pair of nonempty subsets of a modular space . A best proximity point of is a point satisfying the condition: . In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.

scholarly journals Best proximity point theorems for proximal multi-valued contractions

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1889-1897
Author(s):  
Nuttawut Bunlue ◽  
Yeol Cho ◽  
Suthep Suantai
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Best Proximity Points

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and proximal multi-valued nonexpansive mappings in a Banach space and show the existence of best proximity points for both classes. Further, for proximal multi-valued nonexpansive mappings, we prove a best proximity point theorem on starshape sets. As a consequence, we also obtain some new fixed point theorems. Finally, we give some examples to illustrate our main results.

scholarly journals Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 121
Author(s):  
Karim Chaira ◽  
Mustapha Kabil ◽  
Abdessamad Kamouss ◽  
Samih Lazaiz
Keyword(s):  
Banach Spaces ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Partially Ordered ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Ordered Banach Spaces

In this paper, we give sufficient conditions to ensure the existence of the best proximity point of monotone relatively nonexpansive mappings defined on partially ordered Banach spaces. An example is given to illustrate our results.

scholarly journals Weak proximal normal structure and coincidence quasi-best proximity points

2020 ◽  
Vol 21 (2) ◽  
pp. 331
Author(s):  
Farhad Fouladi ◽  
Ali Abkar ◽  
Erdal Karapinar
Keyword(s):  
Point Theorem ◽  
Best Proximity Point ◽  
Normal Structure ◽  
Point Problem ◽  
Best Proximity Points ◽  
Relatively Nonexpansive

We introduce the notion of pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. We study the best proximity point problem for this class of mappings. We also study the same problem for the class of pointwise noncyclic-noncyclic relatively nonexpansive pairs involving orbits. Finally, under the assumption of weak proximal normal structure, we prove a coincidence quasi-best proximity point theorem for pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. Examples are provided to illustrate the observed results.

scholarly journals Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings

2020 ◽  
Vol 53 (1) ◽  
pp. 38-43 ◽  
Author(s):  
Moosa Gabeleh ◽  
Hans-Peter A. Künzi
Keyword(s):  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Studia Math ◽  
Normal Structure ◽  
Projection Algorithm ◽  
Best Proximity Points ◽  
Iteration Sequence ◽  
Cyclic Contractions ◽  
Convergence Method ◽  
Strictly Convex Banach Spaces

AbstractIn this study, at first we prove that the existence of best proximity points for cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic nonexpansive mappings in the setting of strictly convex Banach spaces by using the projection operator. In this way, we conclude that the main result of the paper [Proximal normal structure and nonexpansive mappings, Studia Math. 171 (2005), 283–293] immediately follows. We then discuss the convergence of best proximity pairs for noncyclic contractions by applying the convergence of iterative sequences for cyclic contractions and show that the convergence method of a recent paper [Convergence of Picard's iteration using projection algorithm for noncyclic contractions, Indag. Math. 30 (2019), no. 1, 227–239] is obtained exactly from Picard’s iteration sequence.

C-class functions and pair (F,h) Upper class on common best proximity points results for new proximal C-contraction mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3459-3471
Author(s):  
A.H. Ansari ◽  
Geno Jacob ◽  
D. Chellapillai
Keyword(s):  
Best Proximity Point ◽  
Upper Class ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Common Best Proximity Point

In this paper, using the concept of C-class and Upper class functions we prove the existence of unique common best proximity point. Our main result generalizes results of Kumam et al. [[17]] and Parvaneh et al. [[21]].

scholarly journals Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

2017 ◽  
Vol 59 (1) ◽  
pp. 91-105 ◽  
Author(s):  
C. Kongban ◽  
P. Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Polish Spaces ◽  
Best Proximity Points ◽  
Coupled Best Proximity Point

AbstractIn this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

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