Positive definite solution of the matrix equation X = Q − A*X^−1A + B*X^−1B via Bhaskar-Lakshmikantham fixed point theorem

Purpose: The purpose of this paper is to study the existence and uniqueness of a positive definite solution to the nonlinear matrix equation X = Q − A*X^−1A + B*X^−1B, which is a special stochastic rational Riccati equation arising in stochastic control theory.Methods: Our technique is based on the Bhaskar and Lakshmikantham coupled fixed point theorem.Results: A new result on the existence of a unique positive definite solution is derived. An iterative method is constructed to compute the unique positive definite solution. Finally, some numerical examples are used to show that the iterative method is feasible.Conclusion: Coupled fixed point theory on ordered metric spaces can be a useful tool to solve some classes of nonlinear matrix equations.