Applications of the coupled fixed point theorem to the nonlinear matrix equations

키워드

참고문헌 (15)

1. M. Berzig, "Positive definite solution of the matrix equation <TEX>$X=Q-A*X^{-1}A+B*X^{-1}B$<", TEX> via Bhaskar-Lakshmikantham fixed point theorem, 2012, pp.6, 6~
2. M. Berzig, "An extension of coupled fixed point's concept in higher dimension and applications", Comput. Math. Appl., 63(8), pp.1319~1334 (2012)[DOI]
3. T. Bhaskar, "Fixed point theorems in partially ordered metric spaces and applications", Nonlinear Anal., 65(7), pp.1379~1393 (2006)[DOI]
4. R. Bhatia, "Matrix Analysis, Graduate Texts in Mathematics, Vol. 169" (1997), Springer-Verlag
5. X. Duan, "On the nonlinear matrix equation <TEX>$X-{\Sigma}^m_{i=1}A^*_iX^{{\delta}_i}A_i=Q$<", TEX>, 2008, pp.429(1), 110~121
6. A. Ferrante, "Hermitian solutions of the equation X = Q + N*XN", Linear Algebra Appl., 247, pp.359~373 (1996)[DOI]
7. J. Harjani, "Fixed point theorems for mixed monotone operators and applications to integral equations", Nonlinear Anal., 74(5), pp.1749~1760 (2011)[DOI]
8. V. Hasanov, "Positive definite solutions of the matrix equations <TEX>$X{\pm}A*X^{-q}A=Q$<", TEX>, 2005, pp.404, 166~182
9. M. Huang, "Applications of Hilbert's projective metric to a class of positive nonlinear operators", Linear Algebra Appl., 413(1), pp.202~211 (2006)[DOI]
10. V. Lakshmikantham, "Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces", Nonlinear Anal., 70(12), pp.4341~4349 (2009)[DOI]
11. Y. Lim, "Solving the nonlinear matrix equation <TEX>$X=Q+{\Sigma}^m_{i=1}M_iX^{{\delta}_i}M^*_i$<", TEX> via a contraction principle, 2009, pp.430(4), 1380~1383
12. X. G. Liu, "On the positive definite solutions of the matrix equation <TEX>$X^s{\pm}A^TX^{-t}A=I_n$<", TEX>, 2003, pp.368, 83~97
13. N. V. Luong, "Coupled fixed points in partially ordered metric spaces and application", Nonlinear Anal., 74(3), pp.983~992 (2011)[DOI]
14. B. Meini, "Effcient computation of the extreme solutions of <TEX>$X+A*X^{-1}A=Q$<", TEX> and <TEX>$X-A*X^{-1}A=Q$<, Math. Comput., pp.2001, 71[DOI]
15. A. C. M. Ran, "A fixed point theorem in partially ordered sets and some applications to matrix equations", Proc. Amer. Math. Soc., 132(5), pp.1435~1443 (2004)[DOI]

관련 논문AI추천