On a form of KKM principle and SupInfSup inequalities of von Neumann and of Ky Fan type

DOI10.1016/0022-247X(91)90011-NzbMath0734.47030MaRDI QIDQ810852

Fon-Che Liu

Publication date: 1991

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

compact convex setKKM-principleminimaximal inequality of von Neumann and Ky Fan

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Set-valued operators (47H04)

Related Items (9)

Intersection theorems with applications in optimization ⋮ Foundations of the KKM theory on generalized convex spaces ⋮ A united approach to generalization of the KKM-type theorems related to acyclic maps ⋮ Weakly \(G\)-KKM mappings, \(G\)-KKM property, and minimax inequalities ⋮ A new fixed point theorem and applications ⋮ Remarks on weakly KKM maps in abstract convex spaces ⋮ Another form of KKM type theorem and its applications on generalized convex spaces ⋮ \(W\)-\(G\)-\(F\)-\(KKM\) mapping, intersection theorems and minimax inequalities in \(FC\)-space ⋮ On Ky Fan's section theorem

Cites Work

• On general minimax theorems
• A generalization of Tychonoff's fixed point theorem
• On the use of KKM multifunctions in fixed point theory and related topics
• Some properties of convex sets related to fixed point theorems
• Coincidences for set-valued maps and minimax inequalities
• A minimax inequality and its applications to variational inequalities
• Minimax and fixed point theorems
• Invariant cross-sections and invariant linear subspaces
• Applications of a theorem concerning sets with convex sections
• Nonlinear maximal monotone operators in Banach space
• The fixed point theory of multi-valued mappings in topological vector spaces
• Extensions of two fixed point theorems of F. E. Browder
• On fixed points and variational inequalities—a circular tour
• Invariant subspaces of certain linear operators
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