Abstract
In the present paper, we study a three-step iterative scheme to approximate the fixed points of Hardy and Rogers generalized non-expansive mappings. Some weak and strong convergence results are proved for such mappings in uniformly convex Banach spaces. Further, it is showed numerically that the considered iterative scheme has a better speed of convergence than some known and leading schemes for generalized nonexpansive mappings. The results of this paper are the refinement and generalization of several relevant results in the literature.