Definition:Uniformly Convex Normed Vector Space

Definition
Let $\struct {X, \norm \cdot}$ be a normed vector space.

We say that $X$ is uniformly convex :


 * for every $\epsilon > 0$ there exists $\delta > 0$ such that:
 * whenever $x, y \in X$ have $\norm x = \norm y = 1$ and $\norm {x - y} > \epsilon$, we have:
 * $\ds \norm {\frac {x + y} 2} < 1 - \delta$

Also see

 * Uniformly Convex Normed Vector Space is Strictly Convex
 * Inner Product Space is Uniformly Convex