  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.
