Acyclicity of solution sets to functional inclusions
type: Item
instance of: scholarly article
title: Acyclicity of solution sets to functional inclusions
zbMATH Open document ID: 1012.34011
DOI: 10.1016/S0362-546X(01)00131-6
author: Jan Andres
author: Grzegorz Gabor
author: Lech Górniewicz
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-07-22T00:00:00Z
review text: The first purpose of the authors is to obtain topological properties (compact acyclic, \(R_{\delta}\)) of the fixed-point set of some operators, by using the inverse systems of topological spaces and the limit map technique. Examples illustrating this approach (multivalued Cauchy problems) are also considered. The second aim of the authors is to prove a multivalued generalization of the Aronszajn theorem [\textit{N. Aronszajn}, Ann. Math., II. Ser. 43, 730-738 (1942; Zbl 0061.17106)], by using the Browder-Gupta effective approach [\textit{F. E. Browder} and \textit{C. P. Gupta}, J. Math. Anal. Appl. 26, 390-402 (1969; Zbl 0176.45401)]. An interesting application to a multivalued boundary value problem conclude the second part of the paper.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1751626
zbMATH Keywords: fixed-point
zbMATH Keywords: multivalued map
zbMATH Keywords: functional inclusion
reviewed by: Adrian Petruşel
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00131-6
OpenAlex ID: W2005298029
Wikidata QID: Q126351312
description: scientific article; zbMATH DE number 1751626