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

Fixed Point Theory and Applications volume 2007, Article number: 064874 (2007) Cite this article

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, North China Electric Power University, Baoding, 071003, China

    HY Zhou

  2. Department of Mathematics Education and RINS, College of Natural Sciences, Gyeongsang National University, Chinju, 660-701, South Korea

    YJ Cho & SM Kang

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  1. HY Zhou
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  2. YJ Cho
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  3. SM Kang
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Correspondence to HY Zhou.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhou, H., Cho, Y. & Kang, S. A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings. Fixed Point Theory Appl 2007, 064874 (2007). https://doi.org/10.1155/2007/64874

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