A fixed point theorem for monotone maps and its applications to nonlinear matrix equations
From MaRDI portal
Publication:2337062
DOI10.1155/2015/167049zbMath1492.47054OpenAlexW2279676149WikidataQ59113004 ScholiaQ59113004MaRDI QIDQ2337062
Publication date: 19 November 2019
Published in: Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2015/167049
Fixed-point theorems (47H10) Matrix equations and identities (15A24) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Contractive maps on normed linear spaces and their applications to nonlinear matrix equations
- On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\)
- Solving the nonlinear matrix equation \(X = Q + \sum ^{m}_{i=1}M_{i}X^{\delta _{i}}M^{*}_{i}\) via a contraction principle
- On Hermitian positive definite solution of the matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q\)
- On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
- Perturbation analysis of the matrix equation \(X=Q+A^{\text H}(\widehat X-C)^{-1}A\)
- A nonlinear matrix equation connected to interpolation theory.
- On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
- Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
- On positive definite solutions of the nonlinear matrix equation \(X+A^* X^{-n} A=I\)
- Existence and uniqueness of the positive definite solution for the matrix equation \(X=Q+A^\ast(\hat{X}-C)^{-1}A\)
- Positive definite solutions of the matrix equations \(X\pm A^{\ast}X^{-q} A=Q\)
- Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
- On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
- A fixed point theorem in partially ordered sets and some applications to matrix equations
- A Perturbation Analysis for Nonlinear Selfadjoint Operator Equations
This page was built for publication: A fixed point theorem for monotone maps and its applications to nonlinear matrix equations
