A new iteration process for approximation of fixed points for Suzuki’s generalized non-expansive mappings in uniformly convex Banach spaces

Abstract

This paper is proposed to introduce a new three step iteration process, called AR-iteration process to approximate fixed points of Suzuki’s generalized non-expansive mappings. Some weak and strong convergence results are proved for such mappings in uniformly convex Banach spaces. Moreover, we prove analytically and with numerical example that our iteration process converges faster than some other known iteration processes. To support our claim, we use MATLAB program to approximate fixed points for Suzuki’s generalized non-expansive mappings using our new iteration process and Picard, Thakur, M and Sahu iteration processes. We extend, improve and generalize several known results in the literature of iteration processes of fixed point theory.