Common solution to a pair of non-linear matrix equations via fixed point results
In this paper, we propose an idea to derive some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed with this, we present some interesting common fixed point results involving a couple of altering distance functions along with another control function 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 also point out a probable applicable area of our findings. Finally, we propose an entirely non-trivial example to validate one of the main results with a numerical approximation of convergence of iterated sequence using a diagram.
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