A note on a theorem of Xu and Roach
type: Item
instance of: scholarly article
title: A note on a theorem of Xu and Roach
zbMATH Open document ID: 0927.47037
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-13T00:00:00Z
review text: The author gives a short proof of a theorem due to Xu and Roach concerning a necessary and sufficient condition in order that the steepest descent approximation process associated to a quasi-accretive operator in a uniformly smooth Banach space be convergent.
reviewed by: Ioan I. Vrabie
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 1236176
zbMATH Keywords: steepest descent approximation process
zbMATH Keywords: quasi-accretive operator
zbMATH Keywords: uniformly smooth Banach space
author: Haiyun Zhou
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6070
OpenAlex ID: W1991297805
cites work: Nonlinear mappings of nonexpansive and accretive type in Banach spaces
cites work: Nonlinear semigroups and evolution equations
cites work: An iterative procedure for constructing zeros of accretive sets in Banach spaces
cites work: A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations
cites work: Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
cites work: Approximating the zeros of accretive operators by the Ishikawa iteration process
cites work: Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption
cites work: Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption
DOI: 10.1006/JMAA.1998.6070
description: scientific article; zbMATH DE number 1236176