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Let K be a nonempty closed convex nonexpansive retract of a uniformly convex  Banach space E with P as a nonexpansive retraction. Let T : K → E be non-self  asymptotically nonexpansive in the intermediate sense mapping with F(T) = O.  Let {αni}, {βni} and {γni} are sequences in [0, 1] with αn(i) + βn(i) + γn(i)  = 1 for all i = 1, 2, . . . , N. From arbitrary x1 є K , define the sequence  {xn } iteratively by (8), where {u(i) } for all i = 1, 2, . . . , N are  bounded sequences in K with P∞ u(i) < ∞. (i) If the dual E

Convergence theorems of finite-step iteration with errors for non-self asymptotically nonexpansive in the intermediate sense mappings