Approximation of fixed points of strictly pseudocontractive mappings on arbitrary closed, convex sets in a Banach space

We show that any fixed point of a Lipschitzian, strictly pseudocontractive mapping T on a closed, convex subset K of a Banach space X is necessarily u nique, and may be norm approximated by an iterative procedure. Our argument provides a convergence rate estimate and removes the boundedness assumptio n on K, generalizing theorems of Liu.