Abstract: Suppose that K is a non-empty subset of uniformly smooth Banach space X.Let T:K→X be a Lipschitz local strcily pseudocontractine mapping.In this paper.the iterative sequence which converges strongly to the unique fixed point of Tis given.A related result deals with the problem that the Ishikawa iteration process canvergesstrongly to a solution of the equation TX-f when T is Lipschitzian and local strongly accretive in X.