Strong convergence theorems for three-step iterations with errors for non-lipschitzian nonself-mappings in Banach spaces *

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X with P is a nonexpansive retraction of X onto C. Let T : C → X be an asymptotically nonexpansive in the intermediate sense nonself-mapping. In this paper, we introduced the three-step iterative sequence for such map with errors. Moreover, we prove that, if T is completely continuous, then the three-step iterative sequences converges strongly to a fixed point of T.