Perimetric contraction on quadrilaterals and related fixed point results

TL;DR

This paper introduces a new class of four-point contractions extending classical fixed point theorems, establishing conditions for fixed points in complete metric spaces, with applications illustrated through examples.

Contribution

It develops a four-point analogue of classical contractions, generalizing fixed point results and unifying various contraction types under a common framework.

Findings

Established fixed point existence under new four-point contraction conditions

Unified classical Banach, Kannan, and Chatterjea contractions as special cases

Provided non-trivial examples demonstrating the theory's applicability

Abstract

In this article, we introduce a four-point analogue of Banach-type, Kannan-type, and Chatterjea-type contractions, and examine their properties. We establish sufficient conditions under which these mappings achieve fixed points in a complete metric space. Notably, the classical Banach contraction principle emerges as a special case of our results. To illustrate our theoretical findings, we present several non-trivial examples.