A Common Fixed Point Theorem For Weakly Compatible Mappings Satisfying Property (E. A)

TL;DR

This paper establishes a new common fixed point theorem for weakly compatible mappings satisfying property (E. A) and weakly contractive conditions, extending and improving previous results in fixed point theory.

Contribution

It introduces a modified theorem that broadens the class of mappings for which common fixed points can be guaranteed, enhancing existing fixed point results.

Findings

Proves existence of common fixed points under new conditions

Extends previous fixed point theorems by relaxing assumptions

Provides a generalized framework for weakly compatible mappings

Abstract

The aim of this paper is to prove the existence of common fixed points for a pair of weakly compatible selfmaps satisfying weakly contractive condition and property (E. A). In this context, first we modify Beg and Abbas theorem (\cite{Beg}, Theorem 2.5). Our results improve the corresponding results of Beg and Abbas