Weak And Strong Convergence Theorems Of Asymptotically Nonexpansive Mappings In Uniformly Covex Banach Spaces

X is a uniformly convex Banach space, (?)≠B(?)X closed and convex subset, and T : B → B is an asymptotically nonexpansive mapping with a nonempty fixed-point set. If X satisfies Opial's condition, then weak convergence theorems to some fixed points of T for the three-step (Mann and Ishikawa) iteration process converges are proved. And if T~m is compact for some m ∈ N, or T is completely continuous, then stong convergence theorems for the three-step (Mann and Ishikawa) iteration process are proved. Thus Mann and Ishikawa iteration process become a specialties situation of three-step iteration process.