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Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces

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  • Ming Tian
  • Xin Jin

Abstract

Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.

Suggested Citation

  • Ming Tian & Xin Jin, 2013. "Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, April.
    • Handle: RePEc:hin:jnlaaa:264910
    DOI: 10.1155/2013/264910
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