The KKM principle in abstract convex spaces: equivalent formulations and applications
type: Item
instance of: scholarly article
title: The KKM principle in abstract convex spaces: equivalent formulations and applications
zbMATH Open document ID: 1214.47042
author: Sehie Park
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-07-13T00:00:00Z
review text: This paper is a valuable contribution to KKM theory. Precisely, the author shows that a sequence of a dozen statements characterize the KKM spaces and are equivalent formulations of the partial KKM principle. As applications, the author adds more than a dozen statements including generalized formulations of the von Neumann minimax theorem, the von Neumann intersection lemma, the Nash equilibrium theorem, and the Fan type minimax inequalities for any KKM spaces. Consequently, this paper unifies and enlarges previously known several proper examples of such statements for particular types of KKM spaces.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 46A16
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 5736427
zbMATH Keywords: abstract convex space
zbMATH Keywords: \(G\)-convex spaces
zbMATH Keywords: KKM space
zbMATH Keywords: (partial) KKM principle
zbMATH Keywords: minimax inequality
zbMATH Keywords: minimax theorem
zbMATH Keywords: Nash equilibrium point
zbMATH Keywords: variational inequality
MaRDI profile type: Publication
full work available at URL: j.na.2010.04.029
OpenAlex ID: W2001391724
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DOI: 10.1016/J.NA.2010.04.029
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description: scientific article; zbMATH DE number 5736427