On Common FIXED Points Of Weakly Compatible Mappings Satisfying `Generalized Condition (B)'

TL;DR

This paper establishes the existence of common fixed points for certain weakly compatible mappings under a generalized condition, extending previous theorems in fixed point theory.

Contribution

It generalizes existing fixed point theorems for weakly compatible mappings satisfying a new generalized condition (B).

Findings

Proves existence of common fixed points under generalized condition (B)

Extends previous theorems by Al-Thagafi and Shahzad, Babu et al.

Provides a broader framework for fixed point results in weakly compatible mappings.

Abstract

We prove the existence of common fixed points for two weakly compatible mappings satisfying a 'generalized condition (B)'. This result generalizes some theorems of Al-Thagafi and Shahzad \cite{AlThagafi2006} and Babu, Sandhya and Kameswari \cite{Babu2008}.