... ⊂ F−1 (y) for each y ∈ Y and K = y Y (P−1 (y) ∩ K),(iv) for each compact subset K of X and for each x∈ K,thereexistsy ∈ Y such thatx∈ cintF−1 (y) ∩ K and K = y Y (cintF−1 (y) ∩ K),(v) ... infx∈Xsup y Y g(x, y) − ε, b = sup y Y infx∈Xq(x, y) +ε. (3.12)Then for each x∈ X, there exists y ∈ Y such that g(x, y) >a,andforeachy ∈ Y, thereexist x∈ X such that q(x, y) <b. Therefore, ... transfer compactly open valued on Y, andsoF ∈G-KKM(X ,Y) . By conditions (i), (ii) , and (iii), we have G-Co(S∗ (y) )⊂H∗ (y) ⊂ G∗ (y) ⊂F∗ (y) foreachy ∈ Y. ApplyingProposition 3.9 and Theorem 3.10,...