New generalizations of basic theorems in the KKM theory

DOI10.1016/J.NA.2011.01.020zbMath1225.47060OpenAlexW1982551764MaRDI QIDQ531693

Sehie Park

Publication date: 19 April 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.2011.01.020

zbMATH Keywords

fixed pointvariational inequalitymaximal elementabstract convex spaceintersectionally closed property

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Set-valued operators (47H04) Fixed-point and coincidence theorems (topological aspects) (54H25) Variational inequalities (global problems) in infinite-dimensional spaces (58E35)

Related Items (8)

Collectively fixed point theorems in noncompact abstract convex spaces with applications ⋮ Applications of some basic theorems in the KKM theory ⋮ Fixed points, maximal elements and equilibria of generalized games in abstract convex spaces ⋮ The Fan minimax inequality implies the Nash equilibrium theorem ⋮ Improving KKM theory on general metric type spaces ⋮ Fixed point theorems and \(L^{*}\)-operators ⋮ Generalized Knaster-Kuratowski-Mazurkiewicz theorem without convex hull ⋮ Function and colorful extensions of the KKM theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A generalization of Tychonoff's fixed point theorem
• Existence of solutions in variational relation problems without convexity
• The KKM principle in abstract convex spaces: equivalent formulations and applications
• Some properties of convex sets related to fixed point theorems
• Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity
• Foundations of the KKM theory on generalized convex spaces
• New topological versions of the Fan-Browder fixed point theorem.
• Ninety years of the Brouwer fixed point theorem
• Applications of a theorem concerning sets with convex sections
• The fixed point theory of multi-valued mappings in topological vector spaces
• Extensions of two fixed point theorems of F. E. Browder
• GENERALIZED KKM MAPS, MAXIMAL ELEMENTS AND ALMOST FIXED POINTS
• ELEMENTS OF THE KKM THEORY ON CONVEX SPACES
• Invariant subspaces of certain linear operators

This page was built for publication: New generalizations of basic theorems in the KKM theory