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

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  • Asgari, Mohammad Sadegh
  • Mousavi, Baharak

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.

Suggested Citation

  • Asgari, Mohammad Sadegh & Mousavi, Baharak, 2015. "Solving a class of nonlinear matrix equations via the coupled fixed point theorem," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 364-373.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:364-373
    DOI: 10.1016/j.amc.2015.02.049
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    References listed on IDEAS

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    1. Engwerda, J.C., 1993. "On the existence of a positive definite solution of the matrix equation X = ATX-1A = I," Other publications TiSEM 9d762863-0dfe-4aeb-8a13-5, Tilburg University, School of Economics and Management.
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