On the derivative of a polynomial
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- by N. K. Govil
- Proc. Amer. Math. Soc. 41 (1973), 543-546
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325932-8
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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 $|z| \leqq K \leqq 1$, then it is known that ${\max _{|z| = 1}}|p’(z)| \geqq (n/(1 + K)){\max _{|z| = 1}}|p(z)|$. In this paper we consider the case when $K > 1$ and obtain a sharp result.References
- 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 236385, DOI 10.1090/S0002-9947-1969-0236385-6
- M. A. Malik, On the derivative of a polynomial, J. London Math. Soc. (2) 1 (1969), 57–60. MR 249583, DOI 10.1112/jlms/s2-1.1.57 G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Vol. 1, Berlin, 1925.
- P. Turan, Über die Ableitung von Polynomen, Compositio Math. 7 (1939), 89–95 (German). MR 228
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 543-546
- MSC: Primary 30A08
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325932-8
- MathSciNet review: 0325932