The purpose of this paper, we modify the Thakur iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish strong and $\Delta$- convergence theorems for mean nonexpansive mappings in uniformly convex hyperbolic spaces. We provide an example of mean nonexpansive mapping which is not nonexpansive mapping. Using this example and some numerical texts, we infer empirically that the Thakur iteration process converges faster than the Abbas, Agarwal, Noor, Ishikawa, and Mann iteration processes.
The purpose of this paper, we modify the Thakur iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish strong and $\Delta$- convergence theorems for mean nonexpansive mappings in uniformly convex hyperbolic spaces. We provide an example of mean nonexpansive mapping which is not nonexpansive mapping. Using this example and some numerical texts, we infer empirically that the Thakur iteration process converges faster than the Abbas, Agarwal, Noor, Ishikawa and Mann iteration process.