An existence theorem for a difference inclusion in general Banach spaces
type: Item
instance of: scholarly article
title: An existence theorem for a difference inclusion in general Banach spaces
zbMATH Open document ID: 0813.47041
DOI: 10.1016/0022-247X(91)90313-O
author: Simeon Reich
author: Itai Shafrir
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: In the present paper the authors have studied the problem of existence of solution of the difference inclusion \[ u_{i+ 1}- 2u_ i+ u_{i- 1}\in C_ i Au_ i+ f_ i,\quad i= 1,2,\dots,\;u_ 0= x,\quad \sup\{| u_ i|: i\geq 0\}< \infty,\tag{1} \] where \(A\) is a nonlinear \(m\)- accretive operator in a Banach space \((X,|.|)\), \(\{u_ i\}\) is a given sequence of positive numbers, and \(\{f_ i\}\) is a given sequence in \(X\). The main result proved in this paper is as follows: Theorem. Let \(X\) be a Banach space and \(A\subset X\times X\) an \(m\)- accretive operator. If problem (1) has a solution for some \(x\) in \(X\), then it has a unique solution for all \(x\) in \(X\). An existence theorem for the quasi-autonomous incomplete Cauchy problem is also given.
reviewed by: B. G. Pachpatte
Mathematics Subject Classification ID: 47B39
zbMATH DE Number: 60987
zbMATH Keywords: existence of solution of the difference inclusion
zbMATH Keywords: nonlinear \(m\)- accretive operator
zbMATH Keywords: existence theorem
zbMATH Keywords: quasi-autonomous incomplete Cauchy problem
MaRDI profile type: Publication
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full work available at URL: 0022-247x(91)90313-o
OpenAlex ID: W2058446065
description: scientific article; zbMATH DE number 60987