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Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces

Abstract

Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.

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Correspondence to Jong Soo Jung.

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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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Jung, J.S. Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces. Fixed Point Theory Appl 2008, 167535 (2008). https://doi.org/10.1155/2008/167535

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  • DOI: https://doi.org/10.1155/2008/167535

Keywords

  • Banach Space
  • Differential Geometry
  • Nonexpansive Mapping
  • Iterative Scheme
  • Computational Biology