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An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Abstract

Let be a nonempty closed convex subset of a reflexive Banach space with a weakly continuous dual mapping, and let be an infinite countable family of asymptotically nonexpansive mappings with the sequence satisfying for each , , and for each . In this paper, we introduce a new implicit iterative scheme generated by and prove that the scheme converges strongly to a common fixed point of , which solves some certain variational inequality.

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Correspondence to Shenghua Wang.

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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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Wang, S., Yu, L. & Guo, B. An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces. Fixed Point Theory Appl 2008, 350483 (2008). https://doi.org/10.1155/2008/350483

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  • DOI: https://doi.org/10.1155/2008/350483

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