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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the derivative of a polynomial

Author: N. K. Govil
Journal: Proc. Amer. Math. Soc. 41 (1973), 543-546
MSC: Primary 30A08
MathSciNet review: 0325932
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Abstract: If $ p(z) = \Sigma_{v = 0}^n {{a_v}{z^v}} $ is a polynomial of degree $ n$ having all its zeros in $ \vert z\vert \leqq K \leqq 1$, then it is known that $ {\max _{\vert z\vert = 1}}\vert p'(z)\vert \geqq (n/(1 + K)){\max _{\vert z\vert = 1}}\vert p(z)\vert$. In this paper we consider the case when $ K > 1$ and obtain a sharp result.

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PII: S 0002-9939(1973)0325932-8
Keywords: Inequalities in the complex domain, polynomials, extremal problems
Article copyright: © Copyright 1973 American Mathematical Society