참고문헌
-
M. Berzig, X. Duan, and B. Samet, 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 (2012), Art. 27, 6 pp. https://doi.org/10.1186/2251-7456-6-6 - M. Berzig and B. Samet, An extension of coupled fixed point's concept in higher dimension and applications, Comput. Math. Appl. 63 (2012), no. 8, 1319-1334. https://doi.org/10.1016/j.camwa.2012.01.018
- T. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), no. 7, 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
- R. Bhatia, Matrix Analysis, Graduate Texts in Mathematics, Vol. 169, Springer-Verlag, New York, 1997.
-
X. Duan, A. Liao, and B. Tang, On the nonlinear matrix equation
$X-{\Sigma}^m_{i=1}A^*_iX^{{\delta}_i}A_i=Q$ , Linear Algebra Appl. 429 (2008), no. 1, 110-121. https://doi.org/10.1016/j.laa.2008.02.014 - A. Ferrante and B. Levy, Hermitian solutions of the equation X = Q + N*XN, Linear Algebra Appl. 247 (1996), 359-373. https://doi.org/10.1016/0024-3795(95)00121-2
- J. Harjani, B. Lopez, and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011), no. 5, 1749-1760. https://doi.org/10.1016/j.na.2010.10.047
-
V. Hasanov, Positive definite solutions of the matrix equations
$X{\pm}A*X^{-q}A=Q$ , Linear Algebra Appl. 404 (2005), 166-182. https://doi.org/10.1016/j.laa.2005.02.024 - M. Huang, C. Huang, and T. Tsai, Applications of Hilbert's projective metric to a class of positive nonlinear operators, Linear Algebra Appl. 413 (2006), no. 1, 202-211. https://doi.org/10.1016/j.laa.2005.08.024
- V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), no. 12, 4341-4349. https://doi.org/10.1016/j.na.2008.09.020
-
Y. Lim, Solving the nonlinear matrix equation
$X=Q+{\Sigma}^m_{i=1}M_iX^{{\delta}_i}M^*_i$ via a contraction principle, Linear Algebra Appl. 430 (2009), no 4, 1380-1383. https://doi.org/10.1016/j.laa.2008.10.034 -
X. G. Liu and H. Gao, On the positive definite solutions of the matrix equation
$X^s{\pm}A^TX^{-t}A=I_n$ , Linear Algebra Appl. 368 (2003), 83-97. https://doi.org/10.1016/S0024-3795(02)00661-4 - N. V. Luong and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011), no. 3, 983-992. https://doi.org/10.1016/j.na.2010.09.055
-
B. Meini, Effcient computation of the extreme solutions of
$X+A*X^{-1}A=Q$ and$X-A*X^{-1}A=Q$ , Math. Comput. 71 (2001), 1189-1204. https://doi.org/10.1090/S0025-5718-01-01368-0 - A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443. https://doi.org/10.1090/S0002-9939-03-07220-4