Solving a class of nonlinear matrix equations via the coupled fixed point theorem

Mohammad Sadegh Asgari and Baharak Mousavi

Applied Mathematics and Computation, 2015, vol. 259, issue C, 364-373

Abstract: We consider a class of nonlinear matrix equations of the type(1)X=Q+∑i=1mAi∗G(X)Ai-∑j=1kBj∗K(X)Bj,where Q is a positive definite matrix, Ai,Bj are arbitrary n×n matrices and G,K are two order-preserving or order-reversing continuous maps from H(n) into P(n). In this paper we first discuss existence and uniqueness of coupled fixed points in a L-space endowed with reflexive relation. Next on the basis of the coupled fixed point theorems, we prove the existence and uniqueness of positive definite solutions to such equations.

Keywords: Coupled fixed point; L-space; Matrix equations; Positive define solution (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:364-373

DOI: 10.1016/j.amc.2015.02.049

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