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  • Research Article
  • Open Access

An approximation method for continuous pseudocontractive mappings

Journal of Inequalities and Applications20062006:28950

https://doi.org/10.1155/JIA/2006/28950

  • Received: 20 March 2006
  • Accepted: 28 May 2006
  • Published:

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).

Keywords

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

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Authors’ Affiliations

(1)
College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China
(2)
Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China

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