Method of monotonization of nonlinear equations in Banach spaces
type: Item
instance of: scholarly article
title: Method of monotonization of nonlinear equations in Banach spaces
zbMATH Open document ID: 0671.47058
DOI: 10.1007/BF01158033
author: V. P. Polityukov
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: Let E be a Banach space with a proper cone, A:E\(\to E\) be a linear bounded operator, and F:E\(\to E\) be a continuous operator. The author suggests a method of two-sided successive approximations for the equation \(u=AF(u)\) of the following form \[ u^{n+1}=(I+\lambda A)^{-1}A(F(u^ n)+\lambda u^ n),\quad u^ 0=\sigma^+,\quad u_{n+1}=(I+\lambda A)^{-1}A(F(u_ n)+\lambda u_ n),\quad u_ 0=\sigma^-, \] where \(<\sigma^-,\sigma^+>\) is a cone segment on which the operator F is \(\lambda\) I-monotonic.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 4098125
zbMATH Keywords: two-sided successive approximations
reviewed by: R. R. Akhmerov
MaRDI profile type: Publication
cites work: Q3218622
description: scientific article; zbMATH DE number 4098125