In the current paper we discussed some applications of f non-expansive and quasi-non-expansive mapping in Banach space and matric space along with strong and weak convergence of the sequence of certain iterates to a fixed point of quasi-non-expansive map. we show that {X_n} converges weakly to a common fixed point of T and I the sequence {X_n } contain a subsequence which converges weakly to a point in K Let {X_nk} and {X_mk}be two subsequences of {X_n} which converges weakly to f and q, respectively. We will show that f=g. Suppose that E satisfies Opial’s condition ans that f ≠ q is in weak limit set of the sequence {X_n}. Then {X_nk} → and {X_mk} → q, respectively since lim┬(n→∞) ΙΙ X_n-f ΙΙ exists for any f ∈ F (T) ∩ F (I) by Opial’s condition.