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Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces

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  • D. R. Sahu
  • Ngai-Ching Wong
  • Jen-Chih Yao

Abstract

Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).

Suggested Citation

  • D. R. Sahu & Ngai-Ching Wong & Jen-Chih Yao, 2013. "Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    • Handle: RePEc:hin:jnlaaa:202095
    DOI: 10.1155/2013/202095
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