Strong and Δ-Convergence of a Faster Iteration Process in Hyperbolic Space

Abstract

Abstract. In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

A one-step implicit iterative process for a finite family of I-nonexpansive mappings in Kohlenbach hyperbolic spaces

“…Later on, some authors discussed the convergence of the iterative process in hyperbolic spaces (see, for example, [14][15][16][17]). Motivated by the above facts, in this paper we define a new algorithm as follows:…”

Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces

“…The iterative construction of fixed points of these mappings is a fascinating field of research. The fixed point problem for one or a family of nonexpansive mappings has been studied in Banach spaces, metric spaces and hyperbolic spaces [1][2][3][4][5][6][7][8][9][10][11][12].…”