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.

Best proximity point theorems for weak cyclic Bianchini contractions

2018 ◽  
Vol 27 (1) ◽  
pp. 71-78
Author(s):  
Mihaela Ancuţa Petric ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Best Proximity Point ◽  
Type Theorem ◽  
Best Proximity Points ◽  
New Class ◽  
Point Type

Following the technique introduced in [Eldred, A. A. and Veeramani, P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006], in this paper we will extend Bianchini’s fixed point theorem to best proximity point type theorem. We introduce a new class of contractive conditions, called weak cyclic Bianchini contractions.

scholarly journals Fixed Point Results of a General Class of Monotone Nonexpansive Mappings in Hyperbolic Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Rida Outass ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Nour-eddine El Harmouchi
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Iterative Process ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Ordered Metric Spaces ◽  
New Class

In this paper, we introduce and study some properties of a new class of generalized monotone nonexpansive mappings in hyperbolic metric spaces. Further, we give some results on the convergence of the Mann iterative process for this class of mappings in hyperbolic ordered metric spaces with some interesting examples.

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 discussion on the coincidence quasi-best proximity points

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2107-2119
Author(s):  
Farhad Fouladi ◽  
Ali Abkar ◽  
Erdal Karapınar
Keyword(s):  
Best Proximity Point ◽  
Point Problem ◽  
Proximal Contraction ◽  
Best Proximity Points ◽  
New Class ◽  
Kannan Contraction

In this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validity of the main result.

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 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 A new hybrid algorithm for global minimization of best proximity points in Hilbert spaces

2019 ◽  
Vol 35 (1) ◽  
pp. 95-102
Author(s):  
RAWEEROTE SUPARATULATORN ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Numerical Experiment ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Nonexpansive Mappings ◽  
Global Minimization ◽  
Best Proximity Points ◽  
New Class

The purpose of this paper is to introduce a new hybrid algorithm for finding a global minimization of best proximity points for a new class of mappings, called best proximally nonexpansive (BPNE), which is weaker than nonself nonexpansive mappings and then prove strong convergence of the proposed method under some suitable conditions in real Hilbert spaces. Finally, some numerical experiment is also given for demonstrating our main result.

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