Common fixed points for $\psi-(\alpha,\beta, m)$-contraction pairs

TL;DR

This paper introduces a new class of contraction pairs called $5-4,5,m$-contraction pairs and proves common fixed point theorems for them under weak compatibility and property (E.A.).

Contribution

It establishes fixed point results for a novel class of contraction pairs, extending existing fixed point theory.

Findings

Proves existence of common fixed points for $5-4,5,m$-contraction pairs.

Shows the importance of weak compatibility and property (E.A.) in fixed point theorems.

Extends fixed point results to new classes of mappings.

Abstract

In this paper we establish some common fixed point theorem for a new class of pair of contractions mappings, called $\psi-(\alpha,\beta, m)$-contraction pairs, which we will assume occasionally weakly compatible and satisfying the property (E.A.).