A new contraction principle on the perimeters of triangles and related results

TL;DR

This paper introduces a novel contraction principle for triangle perimeters in metric spaces, establishing fixed point theorems and exploring the space's completeness properties with illustrative examples.

Contribution

It presents a new contraction mapping on triangle perimeters and derives fixed point results, expanding the theoretical framework in metric space analysis.

Findings

Established a fixed point theorem for the new contraction mapping.

Connected the space's completeness to fixed point existence.

Provided multiple examples illustrating the theoretical results.

Abstract

In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed point of our newly introduced mapping. In support of our result, we present several examples.