Abstract
In this paper we introduce a new iteration process for approximation of fixed points. We numerically compare convergence behavior of our iteration process with other iteration process like M-iteration process. We also prove weak and strong convergence theorems for generalized $\alpha-$nonexpansive mappings by using new iteration process. Furthermore we give an example for generalized $\alpha-$nonexpansive mapping but does not satisfy $(C)$ condition.
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