Iterative approximation of fixed points of Lipschitz pseudocontractive maps

Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., l(p); 1 < p<infinity). Let T be a Lipschitzi an pseudocontractive selfmapping of a nonempty closed convex and bounded su bset K of E and let omega is an element of K be arbitrary. Then the iterati on sequence {z(n)} defined by z(o) is an element of K, z(n+1) = (1 mu (n+1) )omega + mu (n+1yn); (yn) = {1 - alpha (n)}z(n) + alpha (n)Tz(n), converges strongly to a fixed point of T, provided that {mu (n)} and {alpha (n)} hav e certain properties. If E is a Hilbert space, then {z(n)} converges strong ly to the unique fixed point of T closest to omega.