Bernstein's inequality

In the mathematical theory of functional analysis, Bernstein's inequality, named after Sergei Natanovich Bernstein, is defined as follows.

Let P be a polynomial of degree $n$ with derivative P′. Then

$\max(P') \le n\cdot\max(P)$

where we define the maximum of a polynomial to be the maximum value attained within a unit disk:

$\max(X) = \max_{|z| \leq 1} \big|X(z)\big|.$

The inequality is named after Sergei Natanovich Bernstein and finds uses in the field of approximation theory.

This mathematical analysis-related article is a stub. You can help Wikipedia by expanding it.