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

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.