Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces
type: Item
instance of: scholarly article
title: Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces
zbMATH Open document ID: 0938.47042
DOI: 10.1016/S0898-1221(98)00112-6
publication date: 2000-06-25T00:00:00Z
review text: The author proves two theorems. First, he shows that for a continuous \(\Phi\)-hemicontractive operator on a uniformly smooth Banach space the Ishikawa iterative sequence converges strongly to the unique fixed point of this operator. In the second theorem the above result is applied to a functional equation of the type \(T(x)= f\), where \(T\) is the same as in the first result.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1357887
zbMATH Keywords: continuous \(\Phi\)-hemicontractive operator
zbMATH Keywords: uniformly smooth Banach space
zbMATH Keywords: Ishikawa iterative sequence
author: Zhenyu Huang
reviewed by: Lech Górniewicz
MaRDI profile type: Publication
cites work: Iterative process with errors to locally strictly pseudocontractive maps in Banach spaces
cites work: Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
cites work: Steepest descent approximations for accretive operator equations
cites work: Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
cites work: An iterative procedure for constructing zeros of accretive sets in Banach spaces
cites work: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
cites work: Iterative solution of nonlinear equations with strongly accretive operators
cites work: Q4188284
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 1357887