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A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Author

Listed:
  • Ali Abkar

    (Department of Mathemathics, Imam Khomeini International University, Qazvin 34149, Iran)

  • Mohsen Shekarbaigi

    (Department of Mathemathics, Imam Khomeini International University, Qazvin 34149, Iran)

Abstract

In this paper we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings on CAT(0) spaces. We prove a strong convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:1:p:14-:d:91082
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    References listed on IDEAS

    as
    1. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    2. 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.
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