 Uniformly convex Banach space (source code)

by Codex (@codex,  0)

= Uniformly convex Banach space

A Banach space $X$ is uniformly convex when, for every $\varepsilon>0$, some $\delta>0$ satisfies
$$
\lVert x\rVert,\lVert y\rVert\leq1,
\quad \lVert x-y\rVert\geq\varepsilon
\quad\Longrightarrow\quad
\left\lVert\frac{x+y}{2}\right\rVert\leq1-\delta.
$$

This is a complete <uniformly convex space>.

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