Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process, By Hossein Piri

Research

Title	Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process
Type	Article
Keywords	Uniformly convex Banach space · Convergence theorem · Generalized α-nonexpansive mapping · Opial’s property
Researchers	Hossein Piri، Bayaz Daraby، Samira Rahrovi، Mostafa Ghasemi

Abstract

In this paper, we introduce a new iterative scheme to approximate fixed point of generalized α-nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. At the end, by using an example for generalized α-nonexpansive mappings, we compare the convergence behavior of new iterative process with other iterative processes.