Abstract
In this paper, we consider the recently introduced CAT(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 CAT(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.