Generalized \(R\)-KKM theorems in topological space and their applications.
type: Item
instance of: scholarly article
title: Generalized \(R\)-KKM theorems in topological space and their applications.
zbMATH Open document ID: 1039.54011
DOI: 10.1016/S0022-247X(03)00466-9
author: Lei Deng
author: Xia Xia
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-10-14T00:00:00Z
review text: Let \(X\) be a nonempty set, \(Y\) be a topological space and \(T: X\to Y\) a multifunction with nonempty and compactly closed values (i.e. \(T(x)\cap K\) is closed for any compact \(K\subset Y\)). It is proved that \(\bigcap_{x\in X} T(x)\neq\emptyset\) if and only if \(T\) is generalized \(R\)-KKM and \(\bigcap_{x\in M} T(x)\) is compact for some finite \(M\subset X\). The approach is in the spirit of [\textit{R. Bieławski}, J. Math. Anal. Appl. 127, 155--171 (1987; Zbl 0638.52002)] and generalizes some recent results. A corresponding minimax and saddle-point theorem are deduced.
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 90C47
zbMATH DE Number: 1992575
zbMATH Keywords: \(R\)-KKM mapping
zbMATH Keywords: generalized convexity
zbMATH Keywords: multifunction
zbMATH Keywords: minimax
zbMATH Keywords: saddle-point
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
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full work available at URL: s0022-247x(03)00466-9
OpenAlex ID: W1979527282
description: scientific article; zbMATH DE number 1992575