ASYMPTOTIC BEHAVIOR OF NONEXPANSIVE MAPPINGS IN FINITE DIMENSIONAL NORMED SPACES

If X is a finite dimensional real normed space, C is a closed convex subset of X and f : C -> C is nonexpansive with respect to the norm on X, then we show that either f has a fixed point in C or there is a linear functional phi is an element of X* such that lim(k ->infinity) phi(f(k)(x)) = infinity for all x is an element of C.