Relaxed iterative algorithms for generalized mixed equilibrium problems with constraints of variational inequalities and variational inclusions
type: Item
instance of: scholarly article
title: Relaxed iterative algorithms for generalized mixed equilibrium problems with constraints of variational inequalities and variational inclusions
zbMATH Open document ID: 1472.47062
DOI: 10.1155/2014/345212
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7022196
zbMATH Keywords: extragradient-like viscosity iterative algorithm
zbMATH Keywords: Hilbert space
zbMATH Keywords: strong convergence
Wikidata QID: Q59036303
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/345212
OpenAlex ID: W1994385840
cites work: Q5890172
cites work: Q4110807
cites work: An extragradient method for solving split feasibility and fixed point problems
cites work: Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
cites work: Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem
cites work: Relaxed extragradient iterative methods for variational inequalities
cites work: An extragradient-like approximation method for variational inequalities and fixed point problems
cites work: Weak convergence of an iterative method for pseudomonotone variational inequalities and fixed-point problems
cites work: Mann type hybrid extragradient method for variational inequalities, variational inclusions and fixed point problems
cites work: Finding common solutions of a variational inequality, a general system of variational inequalities, and a fixed-point problem via a hybrid extragradient method
cites work: A new hybrid-extragradient method for generalized mixed equilibrium problems, fixed point problems and variational inequality problems
cites work: New relaxed hybrid-extragradient method for fixed point problems, a general system of variational inequality problems and generalized mixed equilibrium problems
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: A new completely general class of variational inclusions with noncompact valued mappings
cites work: Characterization of \(H\)-monotone operators with applications to variational inclusions
cites work: A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
cites work: Hybrid extragradient-like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems
cites work: Iterative approaches to convex feasibility problems in Banach spaces
cites work: Q3998720
cites work: Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
cites work: Iterative Algorithms for Nonlinear Operators
cites work: Relaxed hybrid steepest-descent methods with variable parameters for triple-hierarchical variational inequalities
cites work: Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings
cites work: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
description: scientific article; zbMATH DE number 7022196