A new approach to the approximation of common fixed points of an infinite family of relatively quasinonexpansive mappings with applications
type: Item
instance of: scholarly article
title: A new approach to the approximation of common fixed points of an infinite family of relatively quasinonexpansive mappings with applications
zbMATH Open document ID: 1253.65081
DOI: 10.1155/2012/437430
author: Wei-Qi Deng
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: By using a specific way of choosing the indexes, we propose an iteration algorithm generated by the monotone CQ method for approximating common fixed points of an infinite family of relatively quasinonexpansive mappings. A strong convergence theorem without the stronger assumptions of the AKTT condition and the \(^\ast\)AKTT condition imposed on the involved mappings is established in the framework of Banach space. As application, an iterative solution to a system of equilibrium problems is studied. The result is more applicable than those of other authors with related interest.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6116399
zbMATH Keywords: iteration algorithm
zbMATH Keywords: monotone CQ method
zbMATH Keywords: common fixed points
zbMATH Keywords: relatively quasinonexpansive mappings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/437430
OpenAlex ID: W2116557308
Wikidata QID: Q58695159
cites work: Mean Value Methods in Iteration
cites work: Weak convergence theorems for nonexpansive mappings in Banach spaces
cites work: Projection and proximal point methods: Convergence results and counterexamples.
cites work: An example concerning fixed points
cites work: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
cites work: Monotone CQ iteration processes for nonexpansive semigroups and maximal monotone operators
cites work: Q3999276
cites work: Q4894797
cites work: Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
cites work: Block iterative methods for a finite family of relatively nonexpansive mappings in Banach spaces
cites work: Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces
cites work: A strong convergence theorem for relatively nonexpansive mappings in a Banach space
cites work: Q5465330
cites work: Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space
cites work: Strong convergence theorems for relatively nonexpansive mappings in a Banach space
cites work: Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
cites work: Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings
cites work: Nonlinear functional analysis. Fixed point theory and its applications
cites work: Strong Convergence of a Proximal-Type Algorithm in a Banach Space
cites work: Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
cites work: Q3739782
cites work: Q4366516
Recommended article: A new approximation method for common fixed points of a finite family of generalized asymptotically quasinonexpansive mappings in Banach spaces
Recommended article: Q3416978
Recommended article: Approximating common fixed points of families of quasi-nonexpansive mappings
Recommended article: Q4888579
Recommended article: A new approximation method for common fixed points of a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces
Recommended article: APPROXIMATION OF COMMON FIXED POINTS OF A FAMILY OF ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS
Recommended article: Q5324060
Recommended article: Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces
Recommended article: Approximating a common fixed point of finite family of asymptotically quasi-nonexpansive mappings in Banach spaces
Recommended article: Approximation methods for common fixed points of infinite countable family of nonexpansive mappings
description: scientific article; zbMATH DE number 6116399