Generalizations of the KKM type theorems on generalized convex spaces (Q1390144)

The authors give a KKM type theorem in generalized convex spaces for admissible multimaps in the sense of the first author [Bull. Aust. Math. Soc. 51, No. 2, 263-272 (1995; Zbl 0822.47049)]. Following X. P. Ding [the first author, Numer. Funct. Anal. Optimization 15, No. 1-2, 105-119 (1994; Zbl 0813.47064)] the authors extend their result to transfer compactly closed-valued multimaps, presenting as applications a coincidence theorem, a matching theorem and an equilibrium problem.