Consider the nonlinear matrix equation X-A*XpA-B*X-qB=I (0<p,q<1). By using the fixed point theorem for mixed monotone operator in a normal cone, we prove that the equation with 0<p,q<1 always has the unique positive definite solution. Two different iterative methods are given, including the basic fixed point iterative method and the multi-step stationary iterative method. Numerical examples show that the iterative methods are feasible and effective.
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