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

Mostafa Bachar and Mohamed Amine Khamsi
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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

Mathematics, 2019, vol. 7, issue 11, 1-10

Abstract: In this paper, we consider the recently introduced C A T p ( 0 ) , where the comparison triangles belong to ? 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.

Keywords: fixed point; generalized CAT(0) spaces; Hadamard metric spaces; hyperbolic metric spaces; Lipschitzian mapping; modified Mann iteration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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