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Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces

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  • Yali Li
  • Jianjun Liu
  • Lei Deng

Abstract

Let be a nonempty closed convex subset of a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, a generalized asymptotically nonexpansive self-mapping semigroup of , and a fixed contractive mapping with contractive coefficient . We prove that the following implicit and modified implicit viscosity iterative schemes defined by and strongly converge to as and is the unique solution to the following variational inequality: for all .

Suggested Citation

  • Yali Li & Jianjun Liu & Lei Deng, 2008. "Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-10, December.
    • Handle: RePEc:hin:jijmms:687815
    DOI: 10.1155/2008/687815
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    Cited by:

    1. Bashir Ali & G. C. Ugwunnadi, 2012. "Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, July.

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