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 XU has the Kadec]Klee property, C a bounded closed convex subset of X, and Ts T t.: tg w0, `.4 a one-parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense. We show that every continuous almost orbit of T is weakly almost convergent to a common fixed point of T. A discrete version of our main result is also included.