Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps

Let E be a real q-uniformly smooth Banach space which is also uniformly convex (for example, Lp or p spaces, 1 < p <∞), and K a nonempty closed convex (not necessarily bounded) subset of E. Let T :K → K be a k-strictly asymptotically pseudocontractive map with a nonempty fixed-point set. It is proved that (I −T ) is demiclosed at 0. Furthermore, weak and strong convergence of an averaging iteration method to a fixed point of T are proved. © 2006 Elsevier Inc. All rights reserved