Common Fixed Points for Weakly Compatible Mappings via Bivariate Auxiliary Functions

TL;DR

This paper introduces new fixed point theorems for weakly compatible mappings using bivariate auxiliary functions, extending classical results without requiring continuity and only assuming completeness of one image set.

Contribution

It develops fixed point theorems for weakly compatible mappings with bivariate auxiliary functions, broadening applicability beyond classical continuity assumptions.

Findings

Theorems do not require continuity of mappings.

Only one image set needs to be complete.

Results unify and extend existing fixed point theorems.

Abstract

We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness of only one image set. The use of two-variable auxiliary functions allows us to unify and extend various existing fixed point theorems in metric spaces.