Journal of Inequalities and Applications
Volume 7 (2002), Issue 5, Pages 623-631

On growth of polynomials

N. K. Govil

Department of Mathematics, Auburn University, 36849-5310, AL, USA

Received 28 December 2000; Revised 28 March 2001

Copyright © 2002 N. K. Govil. 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.


Let p(z)=v=0navzv be a polynomial of degree n, M(p,R)=max|z|=R1|p(z)| and ||p||=max|z|=1|p(z)|. If p(z)0 in |z|<1, then according to a well known result of Ankeny and Rivlin, M(p,R){(Rn+1)/2}||P|| for R1. In this paper, we generalize and sharpen this and some other related inequalities by considering polynomials having no zeros in |z|<K, K1.