scholarly journals Corrigendum to the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings”

2021 ◽  
Vol 54 (1) ◽  
pp. 9-10
Author(s):  
Moosa Gabeleh
Keyword(s):  
Nonexpansive Mappings ◽  
Short Note ◽  
Best Proximity Points

Abstract The purpose of this short note is to present a correction of the proof of the main result given in the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings,” Demonstr. Math. 53 (2020), 38–43.

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 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 Convergence and Best Proximity Points for Generalized Contraction Pairs

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 176 ◽  
Author(s):  
Slah Sahmim ◽  
Abdelbasset Felhi ◽  
Hassen Aydi
Keyword(s):  
Nonexpansive Mappings ◽  
Approximate Solutions ◽  
Vector Spaces ◽  
Generalized Contraction ◽  
Best Proximity Points ◽  
Global Optimal ◽  
Normed Vector

This paper is devoted to studying the existence of best proximity points and convergence for a class of generalized contraction pairs by using the concept of proximally-complete pairs and proximally-complete semi-sharp proximinal pairs. The obtained results are generalizations of the result of Sadiq Basha (Basha, S., Best proximity points: global optimal approximate solutions, J. Glob. Optim. 2011, 49, 15–21) As an application, we give a result for nonexpansive mappings in normed vector spaces.

Strong convergence of approximants to best proximity points of nonself nonexpansive mappings

2019 ◽  
Vol 28 (2) ◽  
pp. 377-385
Author(s):  
T. Piramatchi ◽  
S. Jamal Fathima ◽  
V. Sankar Raj
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Best Proximity Points

scholarly journals Approximation of Fixed Points and Best Proximity Points of Relatively Nonexpansive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel De La Sen ◽  
Azhar Ulhaq
Keyword(s):  
Hilbert Space ◽  
Fixed Points ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Convergence Result ◽  
Relatively Nonexpansive Mapping ◽  
Von Neumann ◽  
Best Proximity Points ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

In this article, we study the Agarwal iterative process for finding fixed points and best proximity points of relatively nonexpansive mappings. Using the Von Neumann sequence, we establish the convergence result in a Hilbert space framework. We present a new example of relatively nonexpansive mapping and prove that its Agarwal iterative process is more efficient than the Mann and Ishikawa iterative processes.

scholarly journals A short note on the equivalence between ‘best proximity’ points and ‘fixed point’ results

2014 ◽  
Vol 2014 (1) ◽  
pp. 246 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Short Note ◽  
Best Proximity Points
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