Some convergence theorems of the Mann iteration for monotone \(\alpha\)-nonexpansive mappings

DOI10.1016/j.amc.2016.04.011zbMath1410.47015OpenAlexW2416823234WikidataQ59306854 ScholiaQ59306854MaRDI QIDQ1733547

Poom Kumam, Yisheng Song, Yeol Je Cho, Khanittha Promluang

Publication date: 21 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2016.04.011

zbMATH Keywords

convergencefixed pointMann iterationordered Banach spacemonotone \(\alpha\)-nonexpansive mapping

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear accretive operators, dissipative operators, etc. (47H06) Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Fixed-point theorems (47H10) Set-valued operators (47H04) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Common fixed points approximation of two generalized alpha nonexpansive mappings in partially ordered uniformly convex Banach space ⋮ Convergence analysis of an accelerated iteration for monotone generalized \(\alpha\)-nonexpansive mappings with a partial order ⋮ Unnamed Item ⋮ A modified iterative algorithm for finding a common element in Hilbert space ⋮ Weak and Strong Convergence Theorems ofG-Monotone Nonexpansive Mapping in Banach Spaces with a Graph ⋮ Fixed point approximation of monotone nonexpansive mappings in hyperbolic spaces ⋮ Successive approximations for common fixed points of a family of \(\alpha \)-nonexpansive mappings ⋮ Generalized \(\alpha\)-nonexpansive mappings in Banach spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Approximating Fixed Points of Suzuki $$(\alpha ,\beta )$$-Nonexpansive Mappings in Ordered Hyperbolic Metric Spaces ⋮ Iterative methods for monotone nonexpansive mappings in uniformly convex spaces ⋮ Unnamed Item ⋮ Strong and weak convergence of Mann iteration of monotone α-nonexpansive mappings in uniformly convex Banach spaces ⋮ Unnamed Item ⋮ Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence and summable almost \(T\)-stability of the random Picard-Mann hybrid iterative process
• Strong convergence for the modified Mann's iteration of \(\lambda-\)strict pseudocontraction
• On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces
• Mann iteration process for monotone nonexpansive mappings
• On Mann-type iteration method for a family of hemicontractive mappings in Hilbert spaces
• Convergence theorems for strict pseudo-contractions in \(q\)-uniformly smooth Banach spaces
• Convergence theorems for \(\lambda \)-strict pseudo-contractions in 2-uniformly smooth Banach spaces
• Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Approximating fixed points of \({\alpha}\)-nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces
• WEAK AND STRONG CONVERGENCE OF MANN'S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS
• Inequalities in Banach spaces with applications
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Mean Value Methods in Iteration

This page was built for publication: Some convergence theorems of the Mann iteration for monotone \(\alpha\)-nonexpansive mappings