STRONG AND Δ-CONVERGENCE OF A FASTER ITERATION PROCESS IN HYPERBOLIC SPACE

Abstract

Abstract. In this article, we first give metric version of an iterationscheme of Agarwal et al. [1] and approximate fixed points of two finitefamilies of nonexpansive mappings in hyperbolic spaces through this iter-ation scheme which is independent of but faster than Mann and Ishikawascheme. Also we consider case of three finite families of nonexpansivemappings. But, we need an extra condition to get convergence. Our con-vergence theorems generalize and refine many know results in the currentliterature. 1. IntroductionThroughout the article, Ndenotes the set of positive integers and I denotesthe set of first N natural numbers. Let (X,d) be a metric space and K bea nonempty subset of X. A selfmap T on K is said to be nonexpansive ifd(Tx,Ty) ≤ d(x,y). Denote by F (T) the set of fixed points of T and byF = ∩ Ni=1 (F (T i ) ∩F (S i )) the set of common fixed points of two finite familiesof mappings {T i : i ∈ I} and {S i : i ∈ I}.We know that Mann and Ishikawa iteration processes are defined for givenx