In this paper, we proposed a new iterative process to approximate fixed point of generalized α-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 wellknown iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized α-nonexpansive mappings in a Banach space.
