Abstract: Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space. Based on some results given by K Tan and H K Xu[1] proved, the convergence of three-step iterations of (L-α) uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space had proved. The results presented extended the corresponding of Xu and Noor[5].

Key words: fixed point, three-step iterations, asymptotically nonexpansive mapping, (L-α) uniform Lipschitz, uniformly convex Banach space, compact subset