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A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings

Abstract

In the paper by Hu in 2008, the author proved a strong convergence result for nonexpansive mappings using a modified Halpern's iteration algorithm. Unfortunately, the case does not guarantee the strong convergence of the sequence . In this note, we provide a counter-example to the theorem.

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Correspondence to Shuang 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. A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings. Fixed Point Theory Appl 2010, 805326 (2010). https://doi.org/10.1155/2010/805326

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  • DOI: https://doi.org/10.1155/2010/805326

Keywords

  • Differential Geometry
  • Nonexpansive Mapping
  • Strong Convergence
  • Computational Biology
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