Convergence theorems of fixed points for asymptotically hemi-pseudocontractive mappings
type: Item
instance of: scholarly article
title: Convergence theorems of fixed points for asymptotically hemi-pseudocontractive mappings
zbMATH Open document ID: 1176.65069
author: Weiping Guo
author: Qi Guo
published in: Applied Mathematics and Computation
publication date: 2009-10-09T00:00:00Z
review text: The authors extend the concept of asymptotically pseudocontractive mapping with nonempty fixed point set by introducing a new concept: the asymptotically hemi-pseudocontractive mapping in Banach space. For finding the fixed point of a mapping \(T\), which is a uniformly \(L\)-Lipshitzian mapping and an asymptotically hemi-pseudocontractive mapping, the authors propose a modified Ishikawa and a modified Mann iteration sequences with mean errors. The main result of the paper gives sufficient and necessary conditions on the strong convergence of the proposed iterations, to a fixed point of the mapping \(T\). An application is also discussed.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5612870
zbMATH Keywords: Banach space
zbMATH Keywords: fixed point
zbMATH Keywords: uniformly L-Lipshitzian mapping
zbMATH Keywords: asymptotically nonexpansive mapping
zbMATH Keywords: asymptotically pseudocontractive mapping
zbMATH Keywords: asymptotically hemi-pseudocontractive mapping
zbMATH Keywords: Ishikawa iteration
zbMATH Keywords: Mann iteration
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: strong convergence
MaRDI profile type: Publication
full work available at URL: j.amc.2009.04.087
OpenAlex ID: W2142852269
cites work: On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
cites work: Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces
cites work: A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
cites work: Iterative sequences for asymptotically quasi-nonexpansive mappings with error member
cites work: Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings.
cites work: Iterative construction of fixed points of asymptotically nonexpansive mappings
DOI: 10.1016/J.AMC.2009.04.087
description: scientific article; zbMATH DE number 5612870