Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1973-0325932-8
MathSciNet review: 0325932
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)
  • [2] M. A. Malik, On the derivative of a polynomial, J. London Math. Soc. (2) 1 (1969), 57-60. MR 40 #2827. MR 0249583 (40:2827)
  • [3] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Vol. 1, Berlin, 1925.
  • [4] P. Turán Ueber die Ableitung von Polynomen, Compositio Math. 7 (1939), 89-95. MR 1, 37. MR 0000228 (1:37b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A08

Retrieve articles in all journals with MSC: 30A08


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0325932-8
Keywords: Inequalities in the complex domain, polynomials, extremal problems
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society