# A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings

- HY Zhou
^{1}Email author, - YJ Cho
^{2}and - SM Kang
^{2}

**2007**:064874

https://doi.org/10.1155/2007/64874

© H. Y. Zhou et al. 2007

**Received: **28 February 2007

**Accepted: **13 April 2007

**Published: **21 May 2007

## Abstract

Suppose that is a nonempty closed convex subset of a real uniformly convex and smooth Banach space with as a sunny nonexpansive retraction. Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences , , respectively. Suppose that is a sequence in generated iteratively by , , for all , where , , and are three real sequences in for some which satisfy condition . Then, we have the following. (1) If one of and is completely continuous or demicompact and , then the strong convergence of to some is established. (2) If is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Fréchet differentiable, then the weak convergence of to some is proved.

## Authors’ Affiliations

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