Open Access

On the derivative and maximum modulus of a polynomial

Journal of Inequalities and Applications20062006:54816

DOI: 10.1155/JIA/2006/54816

Received: 2 October 2004

Accepted: 11 October 2005

Published: 6 February 2006


If is a polynomial of degree , having all its zeros in , then it was proved by Turán that . This result of Turán was generalized by Govil, who proved that if has all its zeros in , , then , . In this paper, we sharpen this, and some other related results.


Authors’ Affiliations

Department of Mathematics, Jamia Millia Islamia
Department of Mathematics, Auburn University


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© K.K. Dewan et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.