Continuous selections for a family of nonconvex-valued mappings with noncompact domain
type: Item
instance of: scholarly article
title: Continuous selections for a family of nonconvex-valued mappings with noncompact domain
zbMATH Open document ID: 0861.54018
DOI: 10.1007/BF02104812
author: A. A. Tolstonogov
author: Vladimir V. Goncharov
published in: Siberian Mathematical Journal
publication date: 1997-05-12T00:00:00Z
review text: The existence of a continuous selection for multifunctions of the form \[ H(x) = F(x) \cap \bigcap^N_{i=1} \bigl(G_i(x) + f_i(x) \cdot B_i \bigr) \] is exhibited. \(H\) acts between a separable metric space \(S\) and the space \(L_1(T,X)\) where \(T\) is a topological space endowed with positive Radon measure adn \(X\) a separable Banach space. \(F\) and \(G_i: S\to L_1(T,X)\) are lsc with closed, decomposable values, \(f_i\) are single-valued lsc functions and \(B_i: =\{x\in L_1(T,X) : P_i(x) <1\}\) where the \(P_i\) constitute a family of continuous seminorms with some special properties. The paper contains applications of such selection and numerous proofs that many particular seminorms are suitable.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 49J24
zbMATH DE Number: 917064
zbMATH Keywords: decomposable subsets
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
cites work: Q3980652
cites work: Continuous selections for a class of non-convex multivalued maps
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full work available at URL: https://doi.org/10.1007/bf02104812
OpenAlex ID: W2079718489
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description: scientific article; zbMATH DE number 917064