A New and Faster Iterative Scheme Including Generalized $alpha$-nonexpansive Mappings in Banach Spaces

In this paper, we proposed a new iterative process to approximate fixed point of generalized $alpha$-nonexpansive mappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process  with other well-known iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized $alpha$-nonexpansive mappings in a  Banach space.