Strong convergence theorems for asymptotically weak \(G\)-pseudo-\(\Psi\)-contractive non-self-mappings with the generalized projection in Banach spaces
type: Item
instance of: scholarly article
title: Strong convergence theorems for asymptotically weak \(G\)-pseudo-\(\Psi\)-contractive non-self-mappings with the generalized projection in Banach spaces
zbMATH Open document ID: 1256.47055
DOI: 10.1155/2012/651304
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary, modified: A new concept of the asymptotically weak \(G\)-pseudo-\(\Psi\)-contractive non-self-mapping \(T : G \mapsto B\) is introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly smooth Banach space. The methods of proof are also different from some past common methods.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6134141
zbMATH Keywords: strong convergence
zbMATH Keywords: asymptotically weak \(G\)-pseudo-\(\Psi\)-contractive non-self-mappings
zbMATH Keywords: generalized projection method
zbMATH Keywords: modified successive approximation method
zbMATH Keywords: modified Mann iteration
zbMATH Keywords: uniformly smooth Banach space
Wikidata QID: Q58695807
author: Yuanheng Wang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/651304
OpenAlex ID: W1990991972
cites work: A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
cites work: Iterative construction of fixed points of asymptotically nonexpansive mappings
cites work: STRONG CONVERGENCE FOR THREE CLASSES OF UNIFORMLY EQUI-CONTINUOUS AND ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS
cites work: Convergence of an Ishikawa-type iteration scheme for a generalized contraction
cites work: Fixed Point Iteration Processes for Asymptotically Nonexpansive Mappings
cites work: Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings
cites work: Hybrid projection algorithms for asymptotically strict quasi-\(\varphi\)-pseudocontractions
cites work: Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
cites work: Q4669364
cites work: The generalized projection operator on reflexive Banach spaces and its applications
cites work: Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities
cites work: Iterative algorithms approach to variational inequalities and fixed point problems
cites work: Modified relaxed extragradient method for a general system of variational inequalities and nonexpansive mappings in Banach spaces
cites work: Q4358791
cites work: Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions
description: scientific article; zbMATH DE number 6134141