Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings

Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F : F T1 ∩ F T2 {x ∈ K : T1x T2x x}/ ∅. Let T1, T2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences {k i n } ⊂ 1,∞ satisfying ∑∞ n 1 k i n − 1 < ∞ i 1, 2 , respectively. For any given x1 ∈ K, suppose that {xn} is a sequence generated iteratively by xn 1 1−αn PT1 yn αn PT2 yn, yn 1−βn xn βn PT1 xn, n ∈ , where {αn} and {βn} are sequences in a, 1 − a for some a ∈ 0, 1 . Under some suitable conditions, the strong and weak convergence theorems of {xn} to a common fixed point of T1 and T2 are obtained.