Gunduz, Birol; Dutta, Hemen

In this paper, we first define nonself total asymptotically I-nonexpansive mappings and nonself total asymptotically I-quasi-nonexpansive mappings. Then, we prove weak and strong convergence theorems of a composite iterative process to a common fixed point of nonself total asymptotically quasi-nonexpansive mappings and nonself total asymptotically I-quasi-nonexpansive mappings, defined on a nonempty closed convex subset of uniformly convex Banach space.