Iterative construction of fixed points of strictly pseudocontractive mappings

Let (E, ‖ • ‖) be a smooth Banach space over the real field and A a nonempty closed bounded convex subset of E. Suppose T : A → A is a uniformly continuous strictly pseudocontractive selfmapping of A. Then, if [math001]satisfies [math001]the iteration process [math001] and [math001] converges strongly to the unique fixed point x of T. This is an improvement of a result of C.E. Chidume who established strong convergence of (x n to x in case E is L p or l p with [math001] making essential use of the inepuality [math001] which is kown to hold in these spaces for all x and y