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.

Best proximity points for p-cyclic summing iterated contractions

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3275-3287 ◽  
Author(s):  
Mihaela Petric ◽  
Boyan Zlatanov
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces ◽  
Cyclic Contractions ◽  
New Type

We generalize the p - summing contractions maps. We found sufficient conditions for these new type of maps, that ensure the existence and uniqueness of best proximity points in uniformly convex Banach spaces. We apply the result for Kannan and Chatterjea type cyclic contractions and we obtain sufficient conditions for these maps, that ensure the existence and uniqueness of best proximity points in uniformly convex Banach spaces.

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.

scholarly journals On the Metric Compactification of Infinite-dimensional Spaces

2018 ◽  
Vol 62 (3) ◽  
pp. 491-507 ◽  
Author(s):  
Armando W. Gutiérrez
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Metric Spaces ◽  
Infinite Dimensional ◽  
Full Characterization ◽  
Geodesic Metric

AbstractThe notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a generalization of the metric compactification that can be applied to infinite-dimensional Banach spaces. Thereafter we give a complete description of the metric compactification of infinite-dimensional $\ell _{p}$ spaces for all $1\leqslant p<\infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.

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 Cyclic Contractions on -Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
E. Karapınar ◽  
A. Yıldız-Ulus ◽  
İ. M. Erhan
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Integral Type ◽  
Cyclic Maps ◽  
Cyclic Contractions

Conditions for existence and uniqueness of fixed points of two types of cyclic contractions defined on -metric spaces are established and some illustrative examples are given. In addition, cyclic maps satisfying integral type contractive conditions are presented as applications.

scholarly journals Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Manuel De la Sen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Convex Banach Space ◽  
Probabilistic Metric Spaces ◽  
Best Proximity Points ◽  
Menger Spaces ◽  
Cyclic Contractions ◽  
Probabilistic Metric

This paper investigates properties of convergence of distances ofp-cyclic contractions on the union of thepsubsets of an abstract setXdefining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points ofp-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of thep-composite mappings restricted to each of thepsubsets in the cyclic disposal are also investigated and some illustrative examples are given.

scholarly journals Related fixed point results for cyclic contractions on G-metric spaces and application

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 853-869 ◽  
Author(s):  
Hassen Aydi ◽  
Abdelbasset Felhi ◽  
Slah Sahmim
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Cyclic Contractions

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

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.

Sign in / Sign up

Export Citation Format

Share Document