Common solution to a pair of non-linear matrix equations via fixed point results

TL;DR

This paper introduces fixed point theorems involving altering distance functions to establish conditions for the existence and uniqueness of positive definite solutions to pairs of non-linear matrix equations.

Contribution

It develops new fixed point results in Banach spaces that lead to sufficient conditions for solving pairs of non-linear matrix equations.

Findings

Established sufficient conditions for solutions' existence and uniqueness.

Provided fixed point theorems involving altering distance functions.

Suggested potential applications in related mathematical problems.

Abstract

In this article, we propose an idea to develop some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed this, we present some interesting common fixed point results involving couple of altering distance functions along with some other control functions in Banach spaces. Based on these results, we deduce some desired sufficient conditions for the existence and uniqueness of a positive definite common solution to the said pair of non-linear matrix equations. We point out a probable applicable area of our findings.