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Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

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  • Juguo Su
  • Yuchao Tang
  • Liwei Liu

Abstract

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

Suggested Citation

  • Juguo Su & Yuchao Tang & Liwei Liu, 2012. "Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, July.
    • Handle: RePEc:hin:jnljam:170540
    DOI: 10.1155/2012/170540
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