The KKM principle in abstract convex spaces: equivalent formulations and applications

DOI10.1016/j.na.2010.04.029zbMath1214.47042OpenAlexW2001391724MaRDI QIDQ984072

Sehie Park

Publication date: 13 July 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.04.029

zbMATH Keywords

variational inequalityminimax theoremminimax inequalityabstract convex space\(G\)-convex spacesNash equilibrium pointKKM space(partial) KKM principle

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Fixed-point theorems (47H10) Set-valued operators (47H04) Fixed-point and coincidence theorems (topological aspects) (54H25) Existence of solutions for minimax problems (49J35) Existence theories for problems in abstract spaces (49J27) Convex sets in topological linear spaces; Choquet theory (46A55) Convex sets in topological vector spaces (aspects of convex geometry) (52A07)

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