ELEMENTS OF THE KKM THEORY ON CONVEX SPACES

DOI10.4134/JKMS.2008.45.1.001zbMath1149.47040MaRDI QIDQ5453731

Sehie Park

Publication date: 3 April 2008

Published in: Journal of the Korean Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

fixed pointminimax theoremequilibrium problemcoincidence pointKKM operator

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) Fixed points and coincidences in algebraic topology (55M20) Convex sets in topological linear spaces; Choquet theory (46A55) Convex sets in topological vector spaces (aspects of convex geometry) (52A07)

Related Items (21)

Collectively fixed point theorems in noncompact abstract convex spaces with applications ⋮ Generalizations of the Nash equilibrium theorem in the KKM theory ⋮ A collectively fixed point theorem in abstract convex spaces and its applications ⋮ Applications of some basic theorems in the KKM theory ⋮ Evolution of the 1984 KKM theorem of Ky Fan ⋮ Fixed points, maximal elements and equilibria of generalized games in abstract convex spaces ⋮ Remarks on some basic concepts in the KKM theory ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fixed point theory of multimaps in abstract convex uniform spaces ⋮ The Fan minimax inequality implies the Nash equilibrium theorem ⋮ Evolution of the minimax inequality of Ky Fan ⋮ Remarks on weakly KKM maps in abstract convex spaces ⋮ Fixed point theorems and \(L^{*}\)-operators ⋮ Equilibrium existence theorems in KKM spaces ⋮ New generalizations of basic theorems in the KKM theory ⋮ Unnamed Item ⋮ The KKM principle in abstract convex spaces: equivalent formulations and applications ⋮ On the von Neumann-Sion minimax theorem in KKM spaces ⋮ Generalized convex spaces, \(L\)-spaces, and \(FC\)-spaces ⋮ Comments on abstract convexity structures on topological spaces

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