... uniform convexity and asymptotic uniform smoothness. For nonreflexive spaces this duality has been investigated in the literature, but it is still not completely understood. Because of its intimate connection to the midpoint inequality whose importance we have already seen in the proof of Proposition...

... controlled by ω(t). It shows that this notion is related to asymptotic uniform smoothness, and that very smooth bumps, and very asymptotically uniformly smooth norms, exist in all asymptotically c₀ spaces. This allows a new approach to results on Γ-almost everywhere Frechet...