A new iteration method for variational inequalities on the set of common fixed points for a finite family of quasi-pseudocontractions in Hilbert spaces

DOI10.1186/1029-242X-2014-218zbMath1372.41011OpenAlexW2129888180WikidataQ59323614 ScholiaQ59323614MaRDI QIDQ2405642

Hai-Yun Zhou, Pei-Yuan Wang

Publication date: 26 September 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2014-218

zbMATH Keywords

variational inequalitieshybrid steepest descent methodstrongly monotone mappingsquasi-pseudocontractions

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items

Three kinds of new hybrid projection methods for a finite family of quasi-asymptotically pseudocontractive mappings in Hilbert spaces ⋮ Applications of accelerated computational methods for quasi-nonexpansive operators to optimization problems ⋮ Three kinds of hybrid algorithms and their numerical realizations for a finite family of quasi-asymptotically pseudocontractive mappings ⋮ Iterative methods for solving a class of monotone variational inequality problems with applications ⋮ Iterative methods for finding the minimum-norm solution of the standard monotone variational inequality problems with applications in Hilbert spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong convergence theorems for a common fixed point of a family of asymptotically \(k\)-strict pseudocontractive mappings
• Common solutions to variational inequalities
• Convergence of hybrid steepest-descent methods for variational inequalities
• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• The common minimal-norm fixed point of a finite family of nonexpansive mappings
• Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Strong convergence theorems for a family of Lipschitz quasi-pseudo-contractions in Hilbert spaces
• A new explicit iteration method for variational inequalities on the set of common fixed points for a finite family of nonexpansive mappings
• Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces
• Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings
• Iterative Methods for Solving Systems of Variational Inequalities in Reflexive Banach Spaces
• Another control condition in an iterative method for nonexpansive mappings
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Convex programming in Hilbert space

This page was built for publication: A new iteration method for variational inequalities on the set of common fixed points for a finite family of quasi-pseudocontractions in Hilbert spaces