Iteration Problem For (L-α) Uniformly Lipschitz Asymptotically Nonexpansive Mapping

In recent years , The convergence of iteration processes has been studied extensively by many authors . Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5]] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space. Inspired by these results, in this paper, we first give the definition of a new mapping ?(L - a) uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space, then construct three-step iterative sequences of (L-a) uniformly Lipschitz asymptotically nonexpansive mapping in this subset . We proved the convergence of this three-step iterative sequences for (L-a) uniformly Lipschitz asymptoticallynonexpansive mapping, Further more, we proved this three-step iterative sequences with an error member converge to fixed points.