Title : ( Positive definite solutions of certain nonlinear matrix equations )
Authors: Z. Mousavi , F. Mirzapour , Mohammad Sal Moslehian ,
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Abstract
We investigate positive definite solutions of nonlinear matrix equations $X-f(\Phi(X))=Q$ and $X-\sum_{i=1}^{m}f(\Phi_i(X))=Q$, where $Q$ is a positive definite matrix, $\Phi$ and $\Phi_i ~~(1\leq i\leq m)$ are positive linear maps on $\mathbb{M}_n(\mathbb{C})$ and $f$ is a nonnegative matrix monotone or matrix anti-monotone function on $[0,\infty)$. In this article, using appropriate inequalities and some fixed point results, we prove the existence of unique positive definite solutions for the mentioned above equations.
Keywords
, Nonlinear matrix equation, matrix monotone, positive definite solution, positive linear map
@article{paperid:1056537,
author = {Z. Mousavi and F. Mirzapour and Sal Moslehian, Mohammad},
title = {Positive definite solutions of certain nonlinear matrix equations},
journal = {Operators and Matrices},
year = {2016},
volume = {10},
number = {1},
month = {July},
issn = {1846-3886},
pages = {113--126},
numpages = {13},
keywords = {Nonlinear matrix equation; matrix monotone; positive definite solution; positive linear map},
}
%0 Journal Article
%T Positive definite solutions of certain nonlinear matrix equations
%A Z. Mousavi
%A F. Mirzapour
%A Sal Moslehian, Mohammad
%J Operators and Matrices
%@ 1846-3886
%D 2016
