Journal of Inequalities and Applications
Volume 7 (2002), Issue 5, Pages 623-631
doi:10.1155/S1025583402000310
On growth of polynomials
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.
Abstract
Let p(z)=∑v=0navzv be a polynomial of degree n, M(p,R)=max|z|=R≥1|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 R≥1. In this paper, we generalize and sharpen this and some other related inequalities by considering polynomials having no zeros in |z|<K, K≥1.