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A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

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  • C. E. Chidume
  • E. U. Ofoedu

Abstract

Let be a real Banach space, and a closed convex nonempty subset of . Let be total asymptotically nonexpansive mappings. A simple iterative sequence is constructed in and necessary and sufficient conditions for this sequence to converge to a common fixed point of are given. Furthermore, in the case that is a uniformly convex real Banach space, strong convergence of the sequence to a common fixed point of the family is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.

Suggested Citation

  • C. E. Chidume & E. U. Ofoedu, 2009. "A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-17, December.
  • Handle: RePEc:hin:jijmms:615107
    DOI: 10.1155/2009/615107
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    Cited by:

    1. Ali Abkar & Mohsen Shekarbaigi, 2017. "A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces," Mathematics, MDPI, vol. 5(1), pages 1-13, February.

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