Fixed point theorem in ordered Banach spaces and applications to matrix equations

DOI10.1007/s11117-016-0396-2zbMath1362.47033OpenAlexW2272055270MaRDI QIDQ346428

Boubakeur Benahmed, Lotfi Mouhadjer

Publication date: 29 November 2016

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-016-0396-2

zbMATH Keywords

monotone iterationmatrix equationsordered Banach spacespositive fixed point

Mathematics Subject Classification ID

Newton-type methods (49M15) Fixed-point theorems (47H10) Matrix equations and identities (15A24) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items (5)

On the nonlinear matrix equation Xp=A+∑i=1mMi∗(B+X−1)−1Mi ⋮ Unnamed Item ⋮ Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points ⋮ Investigation of positive definite solution of nonlinear matrix equation \(X^p=Q+\sum \nolimits_{i=1}^m A_i^*X^{\delta}A_i\) ⋮ Solvability for two forms of nonlinear matrix equations

Cites Work

• Positive fixed points for a class of nonlinear operators and applications
• On the Hermitian positive defnite solution of the nonlinear matrix equation \(X + A^*X ^{-1} A + B^*X ^{-1} B = I\)
• Positive fixed points for nonlinear operators,
• Fixed point theorems in ordered Banach spaces via quasilinearization
• Positive fixed points and eigenvectors of noncompact decreasing operators with applications to nonlinear integral equations
• On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
• The theory of Newton's method
• Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations
• Fixed point theorems in partially ordered metric spaces and applications
• Multiple Positive Solutions of Semilinear Differential Equations with Singularities
• Solutions of nonlinear equations in cones and positive linear operators
• Fixed point theorems in ordered abstract spaces
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• On the Existence of Positive Solutions of Ordinary Differential Equations
• On matrix equations \(X\pm A^*X^{-2}A=I\)
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