Abstract
The main aim of this paper is to introduce a modified Noor iterations scheme to provide a unified approach to the Mann and Ishikawa iteration processes. We study weak and strong convergence of the new iterations scheme of a nonself asymptotically nonexpansive map satisfying a new control condition in uniformly convex Banach spaces. Several recent results about Mann-type and Ishikawa-type iteration schemes for nonself(self) asymptotically nonexpansive maps follow directly and concurrently from our results.
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