Approximations of Fixed Points in the Hadamard Metric Space <i>CAT</i>_p(0)

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.

Keywords

• fixed point
• generalized cat(0) spaces
• hadamard metric spaces
• hyperbolic metric spaces
• lipschitzian mapping
• modified mann iteration