On the Maximal Positive Definite Solution of the Nonlinear Matrix Equation X − ∑ mi = 1 A ∗i X − 1 A i + ∑ nj = 1 B ∗j X − 1 B j = I

In this paper, the existence and uniqueness of the maximal positive definite solution of the nonlinear matrix equation X − ∑mi=1 A∗i X −1 Ai + ∑nj=1 B∗j X −1 B j = I is studied. Our technique is based on the coupled fixed-point theorem. A sufficient condition for the existence of the unique maximal solution of the above nonlinear matrix equation is investigated. Some numerical examples are presented to show the applicability and the effectiveness of our technique