... 100-2115-M-017-001 of the National Science Counci l of the Republic of China.Author details1Department of Mathematics, Honghe University, Yunnan 661100, China2Department of Mathematics, NationalKaohsiung ... ∞)aτ-function. For each x Î X andA ⊆ X, letd(x, A)=infy∈Ad(x, y),andp(x, A)=infy∈Ap(x, y).Denote byN (X)the family of all nonempty subsets of X, C(X)the family of allnonempty closed subsets of ... capable map. Moreover, it i s not hard toverify that for each x Î X,2p(y, Ty ) ≤ ϕ(p(x, y))p(x, Ty)forally ∈ Tx.Therefore, all the assumptions of Theorem 3.1 are satisfied, and we also show thatF(T)...