Positive definite solutions of certain nonlinear matrix equations
Positive definite solutions of certain nonlinear matrix equations
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DOI：
10.7153/oam-10-08
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发表时间：
2016-07
影响因子：
0.5
通讯作者：
Z. Mousavi;F. Mirzapour;M. Moslehian
中科院分区：
文献类型：
--
作者：
Z. Mousavi;F. Mirzapour;M. Moslehian
研究了非线性矩阵方程X−f(Φ(X))=Q和X−∑i=1 f(Φi(X))=Q的正定解，其中Q是正定矩阵，Φ和Φi(1im)是Mn(C)上的正线性映射，f是[0，∞)上的非负矩阵单调或矩阵反单调函数.本文利用适当的不等式和一些不动点结果，证明了上述方程存在唯一正定解。数学学科分类(2010)：15A24。
We investigate positive definite solutions of nonlinear matrix equations X− f (Φ(X))= Q and X −∑i=1 f (Φi(X)) = Q , where Q is a positive definite matrix, Φ and Φi (1 i m) are positive linear maps on Mn(C) and f is a nonnegative matrix monotone or matrix antimonotone function on [0,∞) . 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. Mathematics subject classification (2010): 15A24.