Sufficient conditions for convergence of modified projection-iterative method for equations with weak nonlinearity
type: Item
instance of: scholarly article
title: Sufficient conditions for convergence of modified projection-iterative method for equations with weak nonlinearity
zbMATH Open document ID: 0735.47041
DOI: 10.1007/BF01066188
author: A. Yu. Luchka
published in: Ukrainian Mathematical Journal
publication date: 1992-06-25T00:00:00Z
review text: This article deals with some modification of the well-known convergence conditions of the projective-iterate methods to the equation \(x=f+Tx+\lambda Fx\) with operators \(T,F:\mathbb{X}\to\mathbb{X}\) in a Banach space \(\mathbb{X}=U+V\) that is a direct sum of some of its subspaces \(U\) and \(V\). The corresponding approximations are defined by means of the formulas \(x_ k=f+Tz_ k+\lambda F_{k-1}\) where \(z_ k=x_{k-1}+w_ k\), \(w_ k\in U\), \(x_ k-z_ k\in V\).
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 8058
zbMATH Keywords: projective-iterate methods
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
cites work: Q3943914
description: scientific article; zbMATH DE number 8058