generalized $alpha$-nonexpansive mapping

In this paper, we proposed a new iterative process to approximate fixed point of generalized $alpha$-nonexpansivemappings 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.

In this paper, we obtain a new modified iteration process in the setting of CAT(0) spaces involving generalized $alpha$-nonexpansive mapping. We prove strong and $Delta$ convergence results for approximating fixed point via newly defined iteration process. Further, we reconfirm our results by non trivial example and tables.