Fixed point results for a new three steps iteration process

Abstract

In this paper, we introduce a new three steps iteration process for approximating the fixed point of a contractive like mapping and Suzuki generalized nonexapansive mapping in the frame work of uniformly convex Banach space. Using our iteration process, we state and prove some convergence results for approximating the fixed points of Suzuki generalized nonexpansive mappings. In addition, we show that our proposed iterative scheme converges faster than some existing iterative schemes in the literature and that it is equivalent to the well known Mann iteration method in the sense of convergence. Finally, the stability ($T$-stable, weak $w^2$-stable) and data dependency results for our  proposed iterative scheme are established with an analytical and numerical example  given  to justify our claim.