Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces

In this paper, we introduce and study a class of new modified iterative approximation processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces. By using generalization of Schu rsquo;s lemma and TanXu rsquo;s inequality, some important related properties of this modified iterative approximation are proposed and analyzed. Further, based on the related properties, we prove ∆-convergence and strong convergence of the modified iterative approximating process in hyperbolic spaces. Because a total asymptotically nonexpansive nonself mapping in hyperbolic spaces includes asymptotically nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0) spaces as special cases, the results presented in this paper improve and generalize the corresponding results in the literature.