Abstract
In this article, we develop a faster iteration method, called the A** iteration method, for approximating the fixed points of almost contraction mappings and generalized alpha-nonexpansive mappings. We establish some weak and strong convergence results of the A** iteration method for fixed points of generalized alpha-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w2-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra-Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature.