Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On nearly uniformly convex Banach spaces

J. R. Partingtona1

a1 Pembroke College, Cambridge

A real Banach space (X, xs2016 · xs2016) is said to be uniformly convex (UC) (or uniformly rotund) if for all xs2208 > 0 there is a δ > 0 such that if xs2016x| ≤ 1, xs2016yxs2016 ≤ 1 and xs2016x−yxs2016xs2208, then xs2016(x + y)/2xs2016 ≤ 1− δ.

(Received June 01 1982)