On positive definite solutions of nonlinear matrix equation Xs-A∗X-tA=Q

In this paper, the nonlinear matrix equation Xs-A∗X-tA=Q is investigated. Based on the fixed-point theory, the existence and the uniqueness of the positive definite solution are studied. An effective iterative method to obtain the unique positive definite solution is established given ‖A‖·‖Q-1‖s+ts