Approximating Common Fixed Points of Finite Family of Asymptotically Nonexpansive Non-self Mappings

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1, T2, . . . , TN : K −→ E be N asymptotically nonexpansive nonself mappings with sequences {r n} such that ∑∞ n=1 r n < ∞, for all 1 ≤ i ≤ N and F = ∩i=1F (Ti) 6= φ. Let {α n}, {β n} and {γ n} are sequences in [0, 1] with α n + β i n + γ i n = 1 for all i = 1, 2, . . . , N . From arbitrary x1 ∈ K, define the sequence {xn} iteratively by (6), where {un} are bounded sequences in K with ∑∞ n=1 un < ∞. (i) If the dual E∗ of E has the Kadec-Klee property, then {xn} converges weakly to a common fixed point x∗ ∈ F ; (ii) if {T1, T2, . . . , TN} satisfies condition (B), then {xn} converges strongly to a common fixed point x∗ ∈ F .