On a form of KKM principle and SupInfSup inequalities of von Neumann and of Ky Fan type
type: Item
instance of: scholarly article
title: On a form of KKM principle and SupInfSup inequalities of von Neumann and of Ky Fan type
zbMATH Open document ID: 0734.47030
DOI: 10.1016/0022-247X(91)90011-N
author: Fon-Che Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: This article deals with some modification of the KKM-principle (Knaster- Kuratowski-Maurkiewicz): If X is a compact convex set in a Hausdorff topological vector space, Y is a topological space and S,A: \(X\to Y\) are two mappings for which S is upper semicontinuous and Ax is closed for each \(x\in X\) then either there exists \(x_ 0\in X\) such that \(Ax\cap Sx_ 0\neq \emptyset\) for all \(x\in X\) or S is trappable by \(A^ cx=Y\setminus Ax\). The latter means there are \(x_ 1,...,x_ m\in X\) and \(x\in co\{x_ 1,...,x_ n\}\) such that \(Sx\subseteq A^ cx_ i\) \((i=1,...,n)\). This result allows the author to obtain in a unique way the well-known minimaximal inequality of von Neumann and Ky Fan and some of their analogues and generalizations.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 4214774
zbMATH Keywords: KKM-principle
zbMATH Keywords: compact convex set
zbMATH Keywords: minimaximal inequality of von Neumann and Ky Fan
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214774