Geodesic
Short note on Bernstein's Inequality
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 476-479

Voir la notice de l'article provenant de la source Math-Net.Ru

The famous Bernstein’s inequality estimates the absolute value of a polynomial's derivative on the unit circle via the maximum absolute value of that polynomial over the circle. In this paper, we prove an explicit formula for increment of a polynomial along a ray, which allows to replace the maximum of absolute value over the unit circle by the maximum through the vertices of an inscribed regular polygon. As a consequence, a new proof of a discrete variant of Bernstein’s polynomial inequality is given.
Keywords: Polynomials, Bernstein's inequality, Growth. 
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     author = {S. A. Baba and A. L. Wani},
     title = {Short note on {Bernstein's} {Inequality}},
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S. A. Baba; A. L. Wani. Short note on Bernstein's Inequality. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 476-479. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a32/