A note on best proximity point for proximal contraction

TL;DR

This paper demonstrates that the best proximity point theorem for proximal contractions can be derived using the Banach contraction principle, providing a new perspective on existing results.

Contribution

It shows that the existing best proximity point theorem for proximal contractions can be proved via the Banach contraction principle, simplifying the approach.

Findings

The best proximity point theorem can be proved using Banach contraction principle.

The paper offers a new proof method for existing theorems.

Simplifies the understanding of proximal contractions and their fixed points.

Abstract

In the year 2011, S.Basha \cite{BS} introduced the notion of proximal contraction in a metric space $X$ and study the existence and uniqueness of best proximity point for this class of mappings. Also, the author gave an algorithm to achieve this best proximity point. In this paper, we show that the best proximity point theorem can be proved by Banach contraction principle.