Viscosity iterative algorithms for fixed point problems of asymptotically nonexpansive mappings in the intermediate sense and variational inequality problems in Banach spaces
type: Item
instance of: scholarly article
title: Viscosity iterative algorithms for fixed point problems of asymptotically nonexpansive mappings in the intermediate sense and variational inequality problems in Banach spaces
zbMATH Open document ID: 1422.47066
author: Gang Cai
author: Y. Shehu
author: Olaniyi S. Iyiola
published in: Numerical Algorithms
publication date: 2017-11-17T00:00:00Z
review text: In this paper, a generalized viscosity algorithm for finding a fixed point of an asymptotically nonexpansive mapping in the intermediate sense is introduced, which is also a solution to a variational inequality problem of two inverse-strongly monotone operators in 2-uniformly smooth and uniformly convex Banach spaces. Some strong convergence theorems are given under suitable assumptions imposed on the parameters. Some numerical examples are also given to show the efficiency and implementation of the results.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6808528
zbMATH Keywords: fixed point
zbMATH Keywords: variational inequality
zbMATH Keywords: asymptotically nonexpansive mapping in the intermediate sense
zbMATH Keywords: Banach spaces
zbMATH Keywords: generalized viscosity algorithm
zbMATH Keywords: strong convergence
reviewed by: Zhang Xian
MaRDI profile type: Publication
full work available at URL: s11075-017-0269-1
OpenAlex ID: W2576435978
Wikidata QID: Q112879558
cites work: Convergence theorems for equilibrium problems and fixed point problems of a finite family of asymptotically \(k\)-strictly pseudocontractive mappings in the intermediate sense
cites work: Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces
cites work: Q4366516
cites work: Equilibrium programming using proximal-like algorithms
cites work: Some algorithms for general monotone mixed variational inequalities
cites work: Some developments in general variational inequalities
cites work: On viscosity iterative methods for variational inequalities
cites work: On iterative methods for solving a system of mixed variational inequalities
cites work: Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
cites work: Mixed equilibrium problems and optimization problems
cites work: A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings
cites work: Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems
cites work: Some new algorithms for solving mixed equilibrium problems
cites work: Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method
cites work: Modified extragradient methods for a system of variational inequalities in Banach spaces
cites work: Strong convergence of an iterative algorithm for variational inequalities in Banach spaces
cites work: Iterative algorithms for solving variational inequalities and fixed point problems for asymptotically nonexpansive mappings in Banach spaces
cites work: Asymptotic behavior of contractions in Banach spaces
cites work: Product formulas, nonlinear semigroups, and accretive operators
cites work: Image recovery by convex combinations of sunny nonexpansive retractions
cites work: Viscosity approximation methods for nonexpansive mappings
cites work: A mean ergodic theorem for mappings which are asymptotically nonexpansive in the intermediate sense.
cites work: Strong convergence theorems of a general iterative process for a finite family of \(\lambda \)i-strict pseudo-contractions in q-uniformly smooth Banach spaces
cites work: Strong Convergence of a Proximal-Type Algorithm in a Banach Space
cites work: On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
cites work: Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces
cites work: Some geometric properties related to the fixed point theory for nonexpansive mappings
cites work: Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces
cites work: Semicontractive and semiaccretive nonlinear mappings in Banach spaces
cites work: Q3999276
cites work: Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
cites work: Weak convergence theorems for asymptotically nonexpansive mappings and semigroups
cites work: Q3427728
cites work: On the asymptotic behavior of nonlinear semigroups and the range of accretive operators
cites work: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
cites work: AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS
cites work: On Projection Algorithms for Solving Convex Feasibility Problems
cites work: Inequalities in Banach spaces with applications
DOI: 10.1007/S11075-017-0269-1
description: scientific article; zbMATH DE number 6808528