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An approximation method for continuous pseudocontractive mappings

Abstract

Let be a closed convex subset of a real Banach space, is continuous pseudocontractive mapping, and is a fixed-Lipschitzian strongly pseudocontractive mapping. For any, let be the unique fixed point of. We prove that if has a fixed point and has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then converges to a fixed point of as approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).

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Correspondence to Yisheng Song.

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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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Song, Y., Chen, R. An approximation method for continuous pseudocontractive mappings. J Inequal Appl 2006, 28950 (2006). https://doi.org/10.1155/JIA/2006/28950

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Keywords

  • Banach Space
  • Approximation Method
  • Convex Subset
  • Real Banach Space
  • Unique Fixed Point
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