Eigenvalues and ranges for perturbations of nonlinear accretive and monotone operators in Banach spaces
type: Item
instance of: scholarly article
title: Eigenvalues and ranges for perturbations of nonlinear accretive and monotone operators in Banach spaces
zbMATH Open document ID: 0946.47036
DOI: 10.1155/S1085337597000341
author: Athanassios G. Kartsatos
author: Haiyun Zhou
published in: Abstract and Applied Analysis
publication date: 2000-10-17T00:00:00Z
full work available at URL: https://eudml.org/doc/48540
full work available at URL: issue-3-4.html
review text: The paper concerns perturbation results for \(m\)-accretive and maximal monotone operators. First, \(X\) is an infinite dimensional Banach space, \(T:D(T)\subseteq X\to X\) is an \(m\)-accretive multifunction, and \(C:D(C)\subseteq X\to X\) is a compact function. Suppose \(0\in T(0)\) and \(D\subseteq X\) is an open, bounded neighborhood of \(0\). Under suitable hypotheses, \(0\not\in C(\partial D)\) implies that, for every \(c>0\), there exists \(\lambda>0\) such that \(0\in(T+cI-\lambda C)(\partial D)\). In addition, \(0\not\in T(\partial D)\) implies that there exists \(\lambda>0\) such that \(0\in(T-\lambda C)(\partial D)\) [cf. \textit{Z. Guan} and \textit{A. G. Kartsatos}, Nonlinear Anal., Theory Methods Appl. 27, No. 2, 125-141 (1996; Zbl 0864.47028)]. Second, \(X\) is a reflexive Banach space, \(T:D(T)\subseteq X\to X^*\) ia a maximal monotone multifunction, and \(C:D(C)\subseteq X\to X^*\) is a function. Suppose \(0\in T(0)\) and \(G\subseteq X\) is an open, bounded neighborhood of \(0\). Under suitable hypotheses, \(0\in(T+C)(\overline{G})\) without the assumption that \(0\not\in T(\partial G)\) [cf. \textit{A. G. Kartsatos}, Proc. Am. Math. Soc. 124, No. 6, 1811-1820 (1996; Zbl 0857.47032)].
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1370650
zbMATH Keywords: monotone operator
zbMATH Keywords: accretive operator
zbMATH Keywords: maximal monotone multifunction
reviewed by: Corneliu Ursescu
MaRDI profile type: Publication
OpenAlex ID: W2004472385
description: scientific article; zbMATH DE number 1370650