GENERALIZED α-NONEXPANSIVE MAPPINGS IN HYPERBOLIC SPACES

Abstract

This paper deals with the new iterative algorithm for approximating the fixed point of generalized α-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized α-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.