Geometric Properties, Minimax Inequalities, and Fixed Point Theorems on Convex Spaces

DOI10.2307/2160419zbMath0806.47054OpenAlexW4245726675MaRDI QIDQ4300962

Jong-Sook Bae, Hoo Kyung Kang, Sehie Park

Publication date: 16 February 1995

Full work available at URL: https://doi.org/10.2307/2160419

zbMATH Keywords

minimax inequalitiesselection theoremexistence of maximizable quasiconcave functionsfixed point theorems for upper hemicontinuous multifunctionsKy Fan type geometric property of convex sets

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Existence of solutions for minimax problems (49J35) Fixed points and coincidences in algebraic topology (55M20) Optimality conditions for minimax problems (49K35) Convex sets in topological vector spaces (aspects of convex geometry) (52A07)

Related Items (12)

Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems ⋮ Existence theorems of solutions for a kind of quasi-variational inequalities with monotone type multivalued mapping ⋮ Remarks on saddle points in nonconvex sets ⋮ Coincidences for \(DKT\) maps in Fréchet spaces and minimax inequalities. ⋮ Single and twin coincidence points for multivalued maps in Fréchet spaces ⋮ Equilibria and fixed points of set-valued maps with nonconvex and noncompact domains and ranges ⋮ Existence theorems of solutions for generalized quasi-variational inequalities, a minimax theorem, and a section theorem in the spaces without linear structure ⋮ Generalized Leray-Schauder principles for condensing admissible multifunctions ⋮ On Ky Fan's section theorem ⋮ Approximate selection theorems in \(H\)-spaces with applications ⋮ Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces ⋮ Fixed points of upper semicontinuous mappings in locally G-convex spaces

Cites Work

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• Minimax and fixed point theorems
• A new generalization of the Schauder fixed point theorem
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• Fixed points of weakly inward multis
• Coincidence Theorem and Saddle Point Theorem
• A Further Generalization of the Knaster-Kuratowski-Mazurkiewicz Theorem
• The coincidence problem for compositions of set-valued maps
• An existence theorem for quasiconcave functions with applications
• Fixed points of compact multifunctions
• Existence of maximizable quasiconcave functions on paracompact convex spaces

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