Common fixed point theorems for pairs of subcompatible maps

TL;DR

This paper introduces weaker notions of compatibility and continuity for pairs of maps and proves new common fixed point theorems that extend previous results in the field.

Contribution

It proposes the concepts of subcompatibility and subsequential continuity, broadening the scope of fixed point theorems for pairs of maps.

Findings

Established fixed point theorems under new weaker conditions

Extended results of Jungck and Rhoades (2006)

Extended results of Djoudi and Nisse (2003) and Mbarki (2002)

Abstract

In this paper, we introduce the new concepts of subcompatibility and subsequential continuity which are respectively weaker than occasionally weak compatibilty and reciprocal continuity. With them, we establish several common fixed point theorems which extend corresponding results of Jungck and Rhoades (2006), Djoudi and Nisse (2003) and Mbarki (2002).