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 w2-stable) and data dependency results for our proposed iterative scheme are established
with an analytical and numerical example given to justify our claim.
