Definitions

Uniformly convex space

In mathematics, uniformly convex spaces are common examples of reflexive Banach spaces. These include all Hilbert spaces and the Lp spaces for

Definition

A uniformly convex space is a Banach space so that, for every $epsilon>0$ there is some $delta>0$ so that for any two vectors with $|x|le1$ and $|y|le 1,$

$|x+y|>2-delta$

implies

Intuitively, the center of a line segment inside the unit ball must lie deep inside the unit ball unless the segment is short.