Positive definite solution of a nonlinear matrix equation |
| |
Authors: | Snehasish Bose Sk Monowar Hossein Kallol Paul |
| |
Affiliation: | 1.Department of Mathematics,Jadavpur University,Jadavpur-32,India;2.Department of Mathematics,Aliah University,Kolkata-156,India |
| |
Abstract: | Using fixed point theory, we present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation ({X = Q pm sum^{m}_{i=1}{A_{i}}^*F(X)A_{i}}), where Q is a positive definite matrix, A i ’s are arbitrary n × n matrices and F is a monotone map from the set of positive definite matrices to itself. We show that the presented condition is weaker than that presented by Ran and Reurings [Proc. Amer. Math. Soc. 132 (2004), 1435–1443]. In order to do so, we establish some fixed point theorems for mappings satisfying (({psi, phi}))-weak contractivity conditions in partially ordered G-metric spaces, which generalize some existing results related to (({psi, phi}))-weak contractions in partially ordered metric spaces as well as in G-metric spaces for a given function f. We conclude, by presenting an example, that our fixed point theorem cannot be obtained from any existing fixed point theorem using the process of Jleli and Samet [Fixed Point Theory Appl. 2012 (2012), Article ID 210]. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|