Iterative approximation to common best proximity points of proximally mean nonexpansive mappings in Banach spaces

2020 ◽  
Author(s):  
V. Pragadeeswarar ◽  
R. Gopi
Keyword(s):  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Approximation ◽  
Best Proximity Points

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 Iterative Approximation of Endpoints for Multivalued Mappings in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Nabil Mlaiki
Keyword(s):  
Banach Spaces ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Point Theory ◽  
Iterative Sequence ◽  
Multivalued Mappings ◽  
Weak And Strong Convergence ◽  
Iterative Approximation ◽  
Convergence Results

The purpose of this paper is to introduce the modified Agarwal-O’Regan-Sahu iteration process (S-iteration) for finding endpoints of multivalued nonexpansive mappings in the setting of Banach spaces. Under suitable conditions, some weak and strong convergence results of the iterative sequence generated by the proposed process are proved. Our results especially improve and unify some recent results of Panyanak (J. Fixed Point Theory Appl. (2018)). At the end of the paper, we offer an example to illustrate the 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 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.

scholarly journals The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuanheng Wang ◽  
Xiuping Wu ◽  
Chanjuan Pan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

AbstractIn this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

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