Existence and uniqueness of best proximity points in geodesic metric spaces

2010 ◽  
Vol 73 (4) ◽  
pp. 915-921 ◽  
Author(s):  
Aurora Fernández-León
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Points ◽  
Geodesic Metric

scholarly journals On Best Proximity Points in Metric and Banach Spaces

2011 ◽  
Vol 63 (3) ◽  
pp. 533-550 ◽  
Author(s):  
Rafa Espínola ◽  
Aurora Fernández-León
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Points ◽  
Geodesic Metric ◽  
Cyclic Contractions

Abstract In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We take two different approaches, each one leading to different results that complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with.

scholarly journals Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
M. De La Sen ◽  
Asier Ibeas
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Points

This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points ofp-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mappingT:⋃i∈p-Ai→⋃i∈p-Bi  (p≥2), whereAiandBi,∀i∈p-={1,2,…,p}, are nonempty subsets ofXwhich satisfyTAi⊆Bi,∀i∈p-, such that(X,d)is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed.

scholarly journals Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
M. De la Sen ◽  
E. Karapinar
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Impulsive Differential Equations ◽  
The Self ◽  
Uniformly Convex ◽  
Convergence Properties ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Uniformly Convex Banach Spaces

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

scholarly journals Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Weak Contraction ◽  
Ordered Metric Spaces ◽  
Best Proximity Points ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Expression ◽  
Rational Type

We introduce a generalized proximal weak contraction of rational type for the non-self-map and proved results to ensure the existence and uniqueness of best proximity point for such mappings in the setting of partially ordered metric spaces. Further, our results provides an extension of a result due to Luong and Thuan (2011) and also it provides an extension of Harjani (2010) to the case of self-mappings.

scholarly journals Some results on best proximity points of cyclic Meir-Keeler contraction mappings

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2081-2089 ◽  
Author(s):  
M. Fakhar ◽  
F. Mirdamadi ◽  
Z. Soltani
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Points ◽  
Contraction Mappings

In this paper, we study the existence and uniqueness of best proximity points for cyclic Meir-Keeler contraction mappings in metric spaces with the property W-WUC. Also, the existence of best proximity points for set-valued cyclic Meir-Keeler contraction mappings in metric spaces with the property WUC are obtained

scholarly journals A Note on Best Approximation in 0-Complete Partial Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Marta Demma ◽  
Mohamed Jleli ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Best Approximation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Partial Metric ◽  
Best Proximity Points ◽  
New Concepts ◽  
Partial Metric Spaces

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

scholarly journals Existence of Coupled Best Proximity Points of p-Cyclic Contractions

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Diana Nedelcheva ◽  
Boyan Zlatanov
Keyword(s):  
Wide Class ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Cyclic Contractions ◽  
Ordered Pairs

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

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.

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