Category:Uniformly Convex Normed Vector Spaces

From ProofWiki
Jump to navigation Jump to search

This category contains results about Uniformly Convex Normed Vector Spaces.
Definitions specific to this category can be found in Definitions/Uniformly Convex Normed Vector Spaces.

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


We say that $X$ is uniformly convex if and only if:

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:
$\ds \norm {\frac {x + y} 2} < 1 - \delta$

Pages in category "Uniformly Convex Normed Vector Spaces"

This category contains only the following page.