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The object of this paper is to present a new iteration process. We will show that our process is faster than the known recent iterative schemes. We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings. We also present a numerical example for proving the rate of convergence of our results. Our results improves many known results of the existing literature. [ABSTRACT FROM AUTHOR]