Iterative solution of nonlinear equations with strongly accretive operators
type: Item
instance of: scholarly article
title: Iterative solution of nonlinear equations with strongly accretive operators
zbMATH Open document ID: 0868.47040
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-08-17T00:00:00Z
review text: This article deals with the equation \(Tx=f\) in a real Banach space \(E\) whose dual space is uniformly convex. Under assumptions that the map \(T\) is continuous, strongly accretive, and that \(I-T\) has a bounded range, the convergence is proved of both the Ishikawa and Mann iteration processes to the unique solution of \(Tx=f\). This basic result essentially generalizes earlier results of the author. In addition some explicit error estimates are presented; these estimates are useful for certain choices of the iteration parameters in order to have approximations to the exact solution with prescribed exactness.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H06
zbMATH DE Number: 785127
zbMATH Keywords: strongly accretive
zbMATH Keywords: bounded range
zbMATH Keywords: Ishikawa and Mann iteration processes
author: C. E. Chidume
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
OpenAlex ID: W1970408188
DOI: 10.1006/JMAA.1995.1185
description: scientific article; zbMATH DE number 785127