ITERATIVE CONSTRUCTION OF FIXED-POINTS OF ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS

Let T be a completely continuous and asymptotically nonexpansive self-mapping of a nonempty closed bounded and convex subset of a Hilbert space. Then, under certain conditions, the sequence defined by xn + 1:= αnTn(xn) + (1 - αn) x n converges strongly to some fixed point of T. A similar result is obtained for asymptotically pseudocontractive mappings whose iterates are Lipschitz continuous with respect to some common Lipschitz constant. © 1991.