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Approximations of Fixed Points in the Hadamard Metric Space CAT p (0)

Author

Listed:
  • Mostafa Bachar

    (Department of Mathematics, College of Science, King Saud University, PO. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mohamed Amine Khamsi

    (Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA)

Abstract

In this paper, we consider the recently introduced C A T p ( 0 ) , where the comparison triangles belong to ℓ p , for p ≥ 2 . We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in C A T p ( 0 ) . Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

Suggested Citation

  • Mostafa Bachar & Mohamed Amine Khamsi, 2019. "Approximations of Fixed Points in the Hadamard Metric Space CAT p (0)," Mathematics, MDPI, vol. 7(11), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1088-:d:285662
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