Approximate selection theorems and their applications
type: Item
instance of: scholarly article
title: Approximate selection theorems and their applications
zbMATH Open document ID: 0918.54018
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-02-16T00:00:00Z
review text: Let \(X\) be a paracompact space, \(Y\) a locally convex linear topological space, and \(F:X\to Y\) a multifunction with convex values. \(F\) is called sub-lsc if for each \(x\in X\) and each neighbourhood of zero in \(Y\) there is a \(z\in F(x)\) and a neighbourhood \(U(x)\) of \(x\) in \(X\) such that for each \(y\in U(x)\), \(z\in F(y)+V\). It is proved that \(F\) is sub-lsc if and only if for each neighbourhood \(V\) of zero in \(Y\) there is a continuous \(V\)-approximate selection \(f:X\to Y\), i.e. \(f(x)\in F(x)+V\). Moreover, the paper contains two theorems concerning \(V\)-approximate selections avoiding an usc multifunction \(T\) topologically separated from \(F\), a remark on Michael's selection theorem, a fixed point theorem for lsc multifunctions with compact range and the existence of equilibrium for generalized games.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 26E25
Mathematics Subject Classification ID: 91A44
zbMATH DE Number: 1053552
zbMATH Keywords: approximate selection
zbMATH Keywords: multifunction
zbMATH Keywords: fixed point
zbMATH Keywords: equilibrium
author: Xi Yin Zheng
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5466
OpenAlex ID: W1969572227
cites work: Q3782303
cites work: A selection theorem and its applications
cites work: Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces
cites work: Fixed points of compact multifunctions
cites work: A selection and a fixed point theorem and an equilibrium point of an abstract economy
cites work: Continuous selections. I
cites work: Q5667036
cites work: A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications
cites work: Existence of maximal elements and equilibria in linear topological spaces
cites work: On the existence of equilibrium for abstract economies
DOI: 10.1006/JMAA.1997.5466
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description: scientific article; zbMATH DE number 1053552