A general concept of multiple fixed point for mappings defined on spaces with a distance

TL;DR

This paper introduces a broad concept of multidimensional fixed points in spaces with a distance, extending and unifying existing fixed point theorems to simplify and generalize prior results.

Contribution

It proposes a new, general framework for multidimensional fixed points that simplifies and extends previous theorems in the literature.

Findings

Established new multidimensional fixed point theorems

Unified various existing fixed point results

Extended the scope of fixed point theory in metric spaces

Abstract

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, {\it Multidimensional fixed point theorems in partially ordered complete metric spaces}, J. Math. Anal. Appl. 396 (2012), 536--545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature.