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An approximation method for continuous pseudocontractive mappings

Journal of Inequalities and Applications volume 2006, Article number: 28950 (2006) Cite this article

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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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Yisheng Song

  2. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China

    Rudong Chen

Authors
  1. Yisheng Song
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  2. Rudong Chen
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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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  • DOI: https://doi.org/10.1155/JIA/2006/28950

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