The solution by iteration of nonlinear equations in uniformly smooth Banach spaces
type: Item
instance of: scholarly article
title: The solution by iteration of nonlinear equations in uniformly smooth Banach spaces
zbMATH Open document ID: 0906.47050
author: Chika Moore
author: C. E. Chidume
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-02-18T00:00:00Z
review text: Let \(E\) be a uniformly smooth Banach space and let \(T:D(T)\subseteq E\to E\) be a strong pseudocontraction with an open domain \(D(t)\) in \(E\) and a fixed point \(x^*\in D(T)\). The authors establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point of \(T\). Related results deal with the iterative solution of operator equations of the form \(f\in Tx\) and \(f\in x+\lambda Tx\), \(\lambda>0\), when \(T\) is a set-valued strongly accretive operator. The theorems include the cases in which the operator \(T\) is defined only locally. Explicit error estimates are also given.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 1115444
zbMATH Keywords: explicit error estimates
zbMATH Keywords: uniformly smooth Banach space
zbMATH Keywords: strong pseudocontraction
zbMATH Keywords: fixed point
zbMATH Keywords: strong convergence of the Mann and Ishikawa iterative processes
zbMATH Keywords: iterative solution of operator equations
zbMATH Keywords: set-valued strongly accretive operator
reviewed by: Ulrich Kosel
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5628
OpenAlex ID: W2042409258
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DOI: 10.1006/JMAA.1997.5628
description: scientific article; zbMATH DE number 1115444