Bernstein's inequality (mathematical analysis)
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In the mathematical theory of mathematical 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
where we define the maximum of a polynomial to be the maximum value attained within a unit disk:
The inequality is named after Sergei Natanovich Bernstein and finds uses in the field of approximation theory.
Using the Bernstein's inequality we have for the k:th derivative,
[edit] See also
- Markov brothers' inequality
- Remez inequality
[edit] References
- C. Frappier, Note on Bernstein's inequality for the third derivative of a polynomial, Journal of Inequalities in Pure and Applied Mathematics, Vol. 5, Issue 1, Article 7, 6 pp., 2004. [1]
