On the convergence of fixed points for Lipschitz type mappings in hyperbolic spaces

In this paper, we prove strong and Δ-convergence theorems for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings on hyperbolic space through the S-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal. 8:61-79, 2007) which is faster and independent of the Mann (Proc. Am. Math. Soc. 4:506-510, 1953) and Ishikawa (Proc. Am. Math. Soc. 44:147-150, 1974) iteration processes. Our results generalize, extend, and unify the corresponding results of Abbas et al. (Math. Comput. Model. 55:1418-1427, 2012), Agarwal et al. (J. Nonlinear Convex Anal. 8:61-79, 2007), Dhompongsa and Panyanak (Comput. Math. Appl. 56:2572-2579, 2008), and Khan and Abbas (Comput. Math. Appl. 61:109-116, 2011).