In this paper, we define the class G-KKM(X,Y) consisting of all multifunctions T:X→2^Y which have the strictly generalized KKM property for a generalized convex space (X,D;Γ). Such class contains Park's admissible class as a subclass. We obtain a coincidence theorem for maps in G-KKM(X,Y) and apply it to establish KKM type theorems, fixed point theorems and minimax theorems.

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