Positive Definite Solution of System of Matrix Equations with X−k and Y−l via Coupled Fixed Point Theorem in Partially Ordered Spaces

We establish adequate conditions for the existence and uniqueness of solutions to systems of two matrix equations when the unknown matrices are raised to a power k∈[−1,1]∖{0}. The findings from coupled fixed points for ordered pairs of maps are used. Numerical examples are provided to illustrate the results shown. Some of the known results are the consequence of our acquisitions.