Document Type : Research Paper


1 Department of Mathematics, University of Maragheh, Maragheh, Iran.

2 Department of Mathematics, University of Maragheh, Maragheh, Iran


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.


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