Best proximity results for $p$-proximal contractions on topological spaces

TL;DR

This paper establishes conditions for the existence and uniqueness of best proximity points for topological p-proximal contractions, extending previous results with new theoretical insights and numerical examples.

Contribution

It introduces new sufficient conditions for best proximity points in topological spaces, generalizing existing results in the literature.

Findings

Established existence and uniqueness conditions

Provided numerical examples validating the results

Generalized known results in the field

Abstract

In this article, we investigate for some sufficient conditions for the existence and uniqueness of best proximity points for the topological $p$-proximal contractions and $p$-proximal contractive mappings on arbitrary topological spaces. Moreover, our results are authenticated by a few numerical examples and these generalize some of the known results in the literature.