A contraction principle in semimetric spaces

TL;DR

This paper extends the contraction principle to complete semimetric spaces with additional regularity, exploring fixed point stability and applying results to various generalized metric spaces.

Contribution

It introduces an extension of the contraction principle for semimetric spaces satisfying a regularity condition, broadening fixed point theory.

Findings

Extended contraction principle applicable to regular semimetric spaces

Established fixed point stability in this setting

Provided applications to generalized metric spaces

Abstract

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric spaces that fulfill an extra regularity property. The stability of fixed points is also investigated in this setting. As applications, fixed point results are presented for several important generalizations of metric spaces.