A NEW ITERATIVE PROCESS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

In this paper, we introduce a new iterative process for approximating a common fixed point of a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space. A necessary and sufficient condition for strong convergence of the propose iterative process is established. We give characterization of a uniformly convex metric space with continuous convex structure and by using this characterization, we also prove convergence results of the propose iterative process in a uniformly convex metric space with continuous convex structure. Moreover, we apply our main results to obtain strong convergence theorems in hyperbolic spaces and CAT(0) spaces. Our results generalize and refine many known results in the current literature.