Approximations of fixed points in the Hadamard metric space CATp(0)

Mostafa Bachar, Mohamed Amine Khamsi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we consider the recently introduced CATp(0), where the comparison triangles belong to lp, 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 CATp(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.

Original languageBritish English
Article number1088
JournalMathematics
Volume7
Issue number11
DOIs
StatePublished - 1 Nov 2019

Keywords

  • Fixed point
  • Generalized CAT(0) spaces
  • Hadamard metric spaces
  • Hyperbolic metric spaces
  • Lipschitzian mapping
  • Modified Mann iteration

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