A discussion on best proximity point and coupled best proximity point in partially ordered metric spaces

Binayak S Choudhury,Nikhilesh Metiya,Pulak Konar,Mihai Postolache

doi:10.1186/s13663-015-0423-1

Abstract

AbstractIn this paper we establish some best proximity point results using generalized weak contractions with discontinuous control functions. The theorems are established in metric spaces with a partial order. We view the main problem in the paper as a problem of finding an optimal approximate solution of a fixed point equation. We also discuss several corollaries and give an illustrative example. We apply our result to obtain some coupled best proximity point results.

Highlights

1 Introduction and mathematical preliminaries In this work we consider a problem of global optimization in the context of partially ordered metric spaces
It is a problem of finding the minimum distance between two subsets of a partially ordered metric space
Non-self-maps have been utilized for the said purposes under a category of problems which has been termed the proximity point problems

Summary

Introduction

Introduction and mathematical preliminariesIn this work we consider a problem of global optimization in the context of partially ordered metric spaces. Through a best proximity point result we obtain the global minima of the real valued function x → d(x, Tx) by constraining an approximate solution of x = Tx to satisfy d(x, Tx) = dist(A, B). In the proximity point problems, there are several uses of functions satisfying contraction conditions as, for instances, in [ – ].

Objectives

Results

Conclusion