A mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense

Let X be a uniformly convex Banach space such that its dual X* has the Kade c-Klee property, C a bounded closed convex subset of X, and F = {T(t): t is an element of [0, infinity)} a one-parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense. We show that every c ontinuous almost orbit of F is weakly almost convergent to a common fixed p oint of F. A discrete version of our main result is also included. (C) 2000 Academic Press.