A note on the stability of iteration procedures for strong pseudocontractions and strongly accretive type equations
type: Item
instance of: scholarly article
title: A note on the stability of iteration procedures for strong pseudocontractions and strongly accretive type equations
zbMATH Open document ID: 0984.47047
author: R. Smith
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-05-05T00:00:00Z
review text: In Indian J. Pure Appl. Math. 28, No. 8, 1017-1029 (1997; Zbl 0898.47047) the author proved that certain Mann and Ishikawa iteration procedures are stable with respect to Lipschitz strong pseudocontractions in real Banach spaces. In J. Math. Anal. Appl. 230, 1-10 (1999; Zbl 0921.47053), \textit{H. Y. Zhou} studied, in real uniformly smooth Banach spaces, iteration methods stable with respect to strong pseudocontractions. The author proves by means of a simple example that the main result of Zhou is false without Lipschitz assumptions.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1542477
zbMATH Keywords: Mann and Ishikawa iteration procedures
zbMATH Keywords: Lipschitz strong pseudocontractions
zbMATH Keywords: real uniformly smooth Banach spaces
MaRDI profile type: Publication
OpenAlex ID: W2017617652
cites work: Q3802113
cites work: Q3802112
cites work: Stable iteration procedures for strong pseudo-contractions and nonlinear operator equations of the accretive type
cites work: Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
cites work: Stable iteration procedures for nonlinear pseudocontractive and accretive operators in arbitrary Banach spaces
cites work: Stability of the Mann and Ishikawa iteration procedures for \(\phi\)-strong pseudocontractions and nonlinear equations of the \(\phi\)-strongly accretive type
cites work: Iterative solutions of nonlinear φ-strongly accretive operator equations in arbitrary Banach spaces
cites work: Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type
cites work: An iterative procedure for constructing zeros of accretive sets in Banach spaces
cites work: Fixed point theorems and stability results for fixed point iteration procedures
cites work: Some fixed point iteration procedures
cites work: Fixed point theorems and stability results for fixed point iteration procedures. II
cites work: Stable iteration procedures for strong pseudocontractions and nonlinear equations involving accretive operators without Lipschitz assumption
DOI: 10.1006/JMAA.2000.6993
description: scientific article; zbMATH DE number 1542477