Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

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?)


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: http://dx.doi.org/10.1090/S0002-9939-1973-0325932-8
PII: S 0002-9939(1973)0325932-8
Keywords: Inequalities in the complex domain, polynomials, extremal problems
Article copyright: © Copyright 1973 American Mathematical Society