Generalized KKM-type theorems for weakly generalized KKM mapping with some applications
The authors introduce the notion of weakly generalized KKM mappings for set--valued mappings \(S:X\to 2^Y,\) where \(X\) is a nonempty set and \(Y\) is a topological space, in order to establish some generalized KKM type theorems without any convexity structure. In Section 3 they present some intersection theorems and generalized KKM type theorems. In particular, in Theorem 3.1, they prove that a weakly generalized KKM mapping with nonempty closed values has the finite intersection property. In Section 4 some minimax inequalities are provided, while in Section 5 the authors present an existence theorem for an abstract generalized vector equilibrium problem.
weakly generalized diagonally quasi--convex
scientific article; zbMATH DE number 5700784