New iteration scheme for numerical reckoning fixed points of nonexpansive mappings

Abstract

The purpose of this paper is to introduce a new three step iteration scheme for approximation of fixed points of the nonexpansive mappings. We show that our iteration process is faster than all of the Picard, the Mann, the Agarwal et al., and the Abbas et al. iteration processes. We support our analytic proof by a numerical example in which we approximate the fixed point by a computer using Matlab program. We also prove some weak convergence and strong convergence theorems for the nonexpansive mappings. MSC: 47H09, 47H10.