The contraction principle in extended context

TL;DR

This paper discusses extensions of the Banach Fixed Point Theorem, providing an elementary proof for a known fixed point result and exploring some applications in the context of weaker contractivity assumptions.

Contribution

It offers a simplified proof of a known fixed point theorem within the extended context of weaker contractivity conditions.

Findings

Elementary proof of a fixed point theorem under extended conditions

Applications demonstrating the theorem's utility

Clarification of the contraction principle in broader settings

Abstract

There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting an elementary proof for a known fixed point result. Some applications are also considered.