Some Results for the Family KKM(X,Y) and the Φ-Mapping in FC-Spaces

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