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

Sejong Kim; Hosoo Lee

doi:10.4134/JKMS.j160793

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J. Korean Math. Soc. 2018; 55(1): 73-82

Online first article August 16, 2017 Printed January 1, 2018

https://doi.org/10.4134/JKMS.j160793

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

Sejong Kim, Hosoo Lee

Chungbuk National University, Sungkyunkwan University

Abstract

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Abstract

In this article we consider certain types of nonlinear matrix equations including the stochastic rational Riccati equation and show the existence and uniqueness of the positive definite solution by using Bhaskar-Lakshmikantham's coupled fixed point theorem.

Keywords: mixed monotone property, coupled fixed point theorem

MSC numbers: 47H10, 15B48