On perturbations of accretive operators in Banach spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1002.47027
publication date: 2002-12-26T00:00:00Z
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H14
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 1626232
zbMATH Keywords: \(m\)-accretive operator
zbMATH Keywords: condensing mapping
zbMATH Keywords: fixed point index
zbMATH Keywords: perturbations
zbMATH Keywords: topological degree
zbMATH Keywords: duality mapping
MaRDI profile type: Publication
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author: Li Yang
title: On perturbations of accretive operators in Banach spaces
published in: Nonlinear Functional Analysis and Applications
review text: Let \(X\) be a Banach space, \(A:D(A)\subset X \to 2^X\) be an \(m\)-accretive mapping and \(\Omega\subset X\) be an open bounded subset with \(\overline{\Omega}\cap D(A)\not=\emptyset\). Let \(p\in X\) and \(C:D(A)\cap\overline{\Omega}\to X\) satisfy the condition that \((I-\lambda C)(I+\lambda A)^{-1}:X\to X\) is a continuous condensing mapping for some \(\lambda>0\) and \(C(D(A)\cap \overline{\Omega}\) is bounded. By using the topological degree of condensing mappings, the author proved that \(p\in (A+C)(D(A)\cap\overline{\Omega})\) if there exists \(z\in D(A)\cap\Omega\) such that \(\langle u+Cx-p,j\rangle\geq 0\) for all \(x\in D(A)\cap \partial\Omega\), \(u\in Ax\), and \(j\in J(x-z)\), where \(J\) is the normal duality mapping. The author extended this result in several directions and gave some applications.
reviewed by: Nan-Jing Huang
description: scientific article; zbMATH DE number 1626232