Abstract
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 ϕ ∈ X * such that lim k→∞ ϕ(f k (x)) = ∞ for all x ∈ C.
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