| In this paper, I am going to study three-step iterative solutions of equations for Asymptotically nonexpensive mappings and Asymptotically Pseudo-contractive mappings. My research will improve the main results in reference [10], moreover the iterative conditions in my paper has generalized the uniformly convex space to arbitrary real Banach space; and the three-step iteration with error has been brought in the paper; The reasoning methods in my paper are not the same as reference [10]. The iterative methods of reference [9] also have been generalized from two-step iteration to three-step iteration and three-step iteration with error. |