On Best Proximity Points in metric and Banach spaces

Authors

Abstract:

Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed linear space X and S,T : A∪B → A∪B be two cyclicmappings. Let (A,B) be a nonempty pair in a normed linear space X andS,T : A∪B → A∪B be two cyclic mappings. A point p ∈ A∪B is called acommon best proximity point for the cyclic pair (T,S) provided that∥p − Tp∥ = d(A,B) = ∥p − Sp∥In this paper, we survey the existence, uniqueness and convergence of a com-mon best proximity point for a cyclic weak ST − ϕ-contraction map, whichis equivalent to study of a solution for a nonlinear programming problem inthe setting of uniformly convex Banach spaces. We will provide examples toillustrate our results.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Existence of best proximity and fixed points in $G_p$-metric spaces

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...

full text

Coincidence Quasi-Best Proximity Points for Quasi-Cyclic-Noncyclic Mappings in Convex Metric Spaces

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...

full text

Common Best Proximity Points in Complex Valued Metric Spaces

In this paper, we obtain the existence and the uniqueness of common best proximity point theorems for non-self mappings between two subsets of a complex valued metric space satisfying certain contractive conditions. Our results supported by some examples.

full text

Coupled best proximity points in ordered metric spaces

In this paper, we prove the existence and uniqueness of a coupled best proximity point for mappings satisfying the proximally coupled contraction condition in a complete ordered metric space. Further, our result provides an extension of a result

full text

Best proximity point theorems in 1/2−modular metric spaces

‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

full text

Non-Archimedean fuzzy metric spaces and Best proximity point theorems

In this paper, we introduce some new classes of proximal contraction mappings and establish  best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 14  issue 1

pages  1- 20

publication date 2020-05-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023