Abstract
We first establish a fixed point theorem for a k-set contraction map on the family KKM(X,X), which does not need to be a compact map. Next, we present the KKM type theorems, matching theorems, coincidence theorems, and minimax theorems on the family KKM(X,Y) and the Φ-mapping in FC-spaces. Our results improve and generalize some recent results.
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