Another Perspective on Chatterjea Contraction

TL;DR

This paper introduces a new class of contractions called m-Chatterjea contractions, extending fixed point results for Chatterjea contractions with additional assumptions, and provides theoretical examples to illustrate their properties.

Contribution

It defines m-Chatterjea contractions, proves fixed point existence and uniqueness under k-continuity, and shows this class strictly contains Chatterjea mappings.

Findings

Fixed point existence and uniqueness for m-Chatterjea contractions.

Examples demonstrating discontinuity at the fixed point.

The new class strictly contains Chatterjea mappings.

Abstract

Inspired by the well-known result stating that if any iterate of a mapping is a Banach contraction on a complete metric space, then the mapping itself possesses a unique fixed point, we investigate that claim for a Chatterjea contraction but by retaining the left-hand side of the inequality as per the mapping itself. With an additional assumption of k- continuity, the existence and uniqueness of a fixed point is obtained for a new class of contractions, m-Chatterjea contraction, on a complete metric space. Several examples are given in order to substantiate many theoretical claims such as discontinuity at the unique limit point of the iterative sequence, as well as examples demonstrating that this new class strictly contains the class of Chatterjea mappings.