Existence Theorems for Generalized Asymptotically Nonexpansive Mappings in Uniformly Convex Metric Spaces

We prove the fixed point property for generalized asymptotically nonexpansive mappings in uniformly convex metric spaces by using the concept of asymptotic center. We also discuss some fixed point theorems in uniformly convex metric spaces. Our results can be applied to obtain the existence of a fixed point of a generalized asymptotically nonexpansive mapping in both uniformly convex hyperbolic spaces and CAT(0) spaces.