Continuous selections for multivalued mappings with closed convex images and applications
type: Item
instance of: scholarly article
title: Continuous selections for multivalued mappings with closed convex images and applications
zbMATH Open document ID: 0987.54023
author: Falun Huang
author: Hongxu Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-02-11T00:00:00Z
review text: Some extensions of the Michael selection theorem are studied. Introducing notions of \(r\)-lower semicontinuity (for \(0<r<1)\) and partial lower semicontinuity (these concepts are too involved to be described here), the authors show that given a paracompact space \(X\), a Banach space \(Y\) if a set-valued \(F:X\to Y\) with closed convex values is \(r\)-lower semicontinuous (or partial lower semicontinuous), then it admits a continuous selection. Usual consequences concerning the existence of fixed points or solutions to differential inclusions involving maps of the above type follow.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1563468
zbMATH Keywords: partial lower semicontinuity
zbMATH Keywords: differential inclusions
reviewed by: Wojciech Kryszewski
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7086
OpenAlex ID: W2027387815
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cites work: Selection theorems under an assumption weaker than lower semi-continuity
cites work: Concepts of lower semicontinuity and continuous selections for convex valued multifunctions
cites work: Michael's theory of continuous selections. Development and applications
cites work: Paraconvexity of the graphs of Lipschitzian functions
cites work: Q4344977
DOI: 10.1006/JMAA.2000.7086
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description: scientific article; zbMATH DE number 1563468