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Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces

Abstract

Let be a left amenable semigroup, let be a representation of as Lipschitzian mappings from a nonempty compact convex subset of a smooth Banach space E into C with a uniform Lipschitzian condition, let be a strongly left regular sequence of means defined on an -stable subspace of , let be a contraction on , and let be sequences in (0, 1) such that , for all n. Let , for all . Then, under suitable hypotheses on the constants, we show that converges strongly to some in , the set of common fixed points of , which is the unique solution of the variational inequality , for all .

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Correspondence to Shahram Saeidi.

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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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Saeidi, S. Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces. Fixed Point Theory Appl 2008, 363257 (2009). https://doi.org/10.1155/2008/363257

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  • DOI: https://doi.org/10.1155/2008/363257

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