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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2010, Volume 7, Pages 476–479
(Mi semr264)
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Research papers
Short note on Bernstein's Inequality
S. A. Baba, A. L. Wani Department of Mathematics, National Institute of Technology,
Srinagar, India
Abstract:
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.
Received November 19, 2010, published December 22, 2010
Citation:
S. A. Baba, A. L. Wani, “Short note on Bernstein's Inequality”, Sib. Èlektron. Mat. Izv., 7 (2010), 476–479
Linking options:
https://www.mathnet.ru/eng/semr264 https://www.mathnet.ru/eng/semr/v7/p476
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