scholarly journals Coincidence best proximity points in convex metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2451-2463 ◽  
Author(s):  
Moosa Gabeleh ◽  
Olivier Otafudu ◽  
Naseer Shahzad
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Convex Metric Spaces

Let T,S : A U B ? A U B be mappings such that T(A) ? B,T(B)? A and S(A) ? A,S(B)?B. Then the pair (T,S) of mappings defined on A[B is called cyclic-noncyclic pair, where A and B are two nonempty subsets of a metric space (X,d). A coincidence best proximity point p ? A U B for such a pair of mappings (T,S) is a point such that d(Sp,Tp) = dist(A,B). In this paper, we study the existence and convergence of coincidence best proximity points in the setting of convex metric spaces. We also present an application of one of our results to an integral equation.

scholarly journals A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 19 ◽  
Author(s):  
Erdal Karapınar ◽  
Mujahid Abbas ◽  
Sadia Farooq
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Zero Set ◽  
Related Literature ◽  
Proximal Contraction ◽  
Best Proximity Points

In this paper, we investigate the existence of best proximity points that belong to the zero set for the α p -admissible weak ( F , φ ) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish φ -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.

scholarly journals Generalized 2-proximal C-contraction mappings in complete ordered 2-metric space and their best proximity points

2020 ◽  
Vol 12 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A.G. Sanatee ◽  
M. Iranmanesh ◽  
L.N. Mishra ◽  
V.N. Mishra
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Contraction Type

In this paper, we extend the concept of best proximity point to 2-metric spaces and prove the existence of such points for contraction type non-self mappings in the setting of complete 2-metric spaces. Also, we presented an example to support our results.

scholarly journals A New Best Approximation Result in (S) Convex Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
M. Sabiri ◽  
J. Mouline ◽  
A. Bassou ◽  
T. Sabar
Keyword(s):  
Metric Space ◽  
Best Approximation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Approximation Result ◽  
Cyclic Contraction ◽  
Convex Structure ◽  
Convex Metric Spaces

Consider a self-mapping T defined on the union of p subsets of a metric space, and T is said to be p cyclic if TAi⊆Ai+1 for i=1,…,p with Ap+1=A1. In this article, we introduce the notion of S convex structure, and we acquire a best proximity point for p cyclic contraction in S convex metric spaces.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

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].

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces

2008 ◽  
Vol 15 (1) ◽  
pp. 39-43
Author(s):  
Ljubomir B. Ćirić ◽  
Nebojša T. Nikolić
Keyword(s):  
Metric Space ◽  
Convex Subset ◽  
Metric Spaces ◽  
Satisfy Condition ◽  
Convex Metric Space ◽  
Convex Metric Spaces ◽  
The Family

Abstract Let (𝑋, 𝑑) be a convex metric space, 𝐶 be a closed and convex subset of 𝑋 and let 𝐵(𝐶) be the family of all nonempty bounded subsets of 𝐶. In this paper some results are obtained on the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings 𝑆,𝑇 : 𝐶 → 𝐵(𝐶) which satisfy condition (2.1) below.

scholarly journals Best proximity points of contractive mappings on a metric space with a graph and applications

2017 ◽  
Vol 18 (1) ◽  
pp. 13
Author(s):  
Asrifa Sultana ◽  
V. Vetrivel
Keyword(s):  
Fixed Point ◽  
Uniqueness Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Existence And Uniqueness Theorem ◽  
Best Proximity Points ◽  
Contractive Mappings

We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent  fixed point and best proximity point results.

scholarly journals Paths in hyperspaces

2003 ◽  
Vol 4 (2) ◽  
pp. 377 ◽  
Author(s):  
Camillo Constantini ◽  
Wieslaw Kubís
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Absolute Retract ◽  
Almost Convex ◽  
Convex Metric Spaces ◽  
Metric Topology ◽  
Hausdorff Metric Topology ◽  
Bounded Sets ◽  
Separable Metric Space

<p>We prove that the hyperspace of closed bounded sets with the Hausdor_ topology, over an almost convex metric space, is an absolute retract. Dense subspaces of normed linear spaces are examples of, not necessarily connected, almost convex metric spaces. We give some necessary conditions for the path-wise connectedness of the Hausdorff metric topology on closed bounded sets. Finally, we describe properties of a separable metric space, under which its hyperspace with the Wijsman topology is path-wise connected.</p>

scholarly journals Random Best Proximity Points for α-Admissible Mappings via Simulation Functions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 262 ◽  
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Simulation Functions

In this paper, we introduce a new concept of random α -proximal admissible and random α - Z -contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces.

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