Some common fixed points results on metric spaces over topological modules

TL;DR

This paper extends fixed point theorems to metric spaces over topological modules, generalizing classical results like the Perov theorem to a broader algebraic setting.

Contribution

It introduces R-metric spaces over topological modules and proves fixed point theorems within this new framework, broadening the scope of fixed point theory.

Findings

Established fixed point theorems in R-module metric spaces

Generalized Perov's theorem to topological R-modules

Provided new tools for analysis in algebraic and topological structures

Abstract

In this paper, we replace the real numbers by a topological R-module and define R-metric spaces $(X,d)$. Also, we prove some common fixed point theorems on R-module metric spaces. We obtain, as a particular case the Perov theorem.