Remarks on some basic concepts in the KKM theory

DOI10.1016/J.NA.2010.10.035zbMath1296.49013OpenAlexW2085289339MaRDI QIDQ631714

Sehie Park

Publication date: 14 March 2011

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.2010.10.035

zbMATH Keywords

fixed point\(H\)-spaceabstract convex spaceKKM type theoremclosed-value multimapgeneralized convex (\(G\)-convex) spaceKKM spacepartial KKM principle

Mathematics Subject Classification ID

Variational inequalities (49J40) Fixed-point theorems (47H10) Set-valued operators (47H04) Selections in general topology (54C65) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (5)

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 ⋮ Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems in \(G\)-convex spaces ⋮ Evolution of the minimax inequality of Ky Fan

Cites Work

• On the use of KKM multifunctions in fixed point theory and related topics
• Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally \(FC\)-uniform spaces
• Generalized KKM-type theorems in GFC-spaces and applications
• Generalized convex spaces, \(L\)-spaces, and \(FC\)-spaces
• Fixed point theorems and existence of equilibrium points of noncompact abstract economies for \(\mathcal L_F^*\)-majorized mappings in FC-spaces
• On the generalized quasi-variational inequality problems
• Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity
• On some generalized quasi-equilibrium problems
• On Ky Fan's section theorem
• The study of existence of equilibria for generalized games without lower semicontinuity in locally topological vector spaces
• New H-KKM theorems and their applications to geometric property, coincidence theorems, minimax inequality and maximal elements
• Foundations of the KKM theory on generalized convex spaces
• A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications
• The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications
• A minimax theorem and two existence theorems of solutions for generalized quasi-variational inequalities in \(H\)-spaces
• Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces
• COMMENTS ON DING'S EXAMPLES OF FC-SPACES AND RELATED MATTERS
• On Nonlinear Variational Inequalities
• G-KKM theorem, minimax inequalities and saddle points
• Some new minimax inequalities and applications to existence of equilibria in H-spaces
• ELEMENTS OF THE KKM THEORY ON CONVEX SPACES
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Remarks on some basic concepts in the KKM theory