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In this article we consider certain types of nonlinear matrix equations including the stochastic rational Riccati equation and show the existence and uniqueness of the positive definite solution by using Bhaskar-Lakshmikantham's coupled fixed point theorem.
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참고문헌 (15)
참고문헌 신청
M. Berzig / 2012 / Positive definite solution of the matrix equation $X=Q-A*X^{-1}A+B*X^{-1}B$ via Bhaskar-Lakshmikantham fixed point theorem / Math. Sci. 6:6
M. Berzig / 2012 / An extension of coupled fixed point's concept in higher dimension and applications / Comput. Math. Appl. 63(8):1319~1334
T. Bhaskar / 2006 / Fixed point theorems in partially ordered metric spaces and applications / Nonlinear Anal. 65(7):1379~1393
R. Bhatia / 1997 / Matrix Analysis, Graduate Texts in Mathematics, Vol. 169 / Springer-Verlag
X. Duan / 2008 / On the nonlinear matrix equation $X-{\Sigma}^m_{i=1}A^*_iX^{{\delta}_i}A_i=Q$ / Linear Algebra Appl. 429(1):110~121
M. Berzig / 2012 / An extension of coupled fixed point's concept in higher dimension and applications / Comput. Math. Appl. 63(8):1319~1334
T. Bhaskar / 2006 / Fixed point theorems in partially ordered metric spaces and applications / Nonlinear Anal. 65(7):1379~1393
R. Bhatia / 1997 / Matrix Analysis, Graduate Texts in Mathematics, Vol. 169 / Springer-Verlag
X. Duan / 2008 / On the nonlinear matrix equation
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