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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.

References [Enhancements On Off] (What's this?)

  • [1] N. K. Govil and Q. I. Rahman, Functions of exponential type not vanishing in a half-plane and related polynomials, Trans. Amer. Math. Soc. 137 (1969), 501-517. MR 38 #4681. MR 0236385 (38:4681)
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Keywords: Inequalities in the complex domain, polynomials, extremal problems
Article copyright: © Copyright 1973 American Mathematical Society

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