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Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces

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  • Chin-Tzong Pang
  • Eskandar Naraghirad

Abstract

We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. It is important to state clearly that the contribution of this paper in relation with the previous works (Marino and Xu, 2006) is a technical method to prove strong convergence theorems of a general iterative algorithm for an infinite family of nonexpansive mappings in Banach spaces. Our results improve and generalize many known results in the current literature.

Suggested Citation

  • Chin-Tzong Pang & Eskandar Naraghirad, 2013. "Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    • Handle: RePEc:hin:jnlaaa:539061
    DOI: 10.1155/2013/539061
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