Journal of Inequalities and Applications 
Volume 7 (2002), Issue 5, Pages 623-631
doi:10.1155/S1025583402000310

On growth of polynomials

N. K. Govil

 Department of Mathematics, Auburn University, 36849-5310, AL, USA
Received 28 December 2000; Revised 28 March 2001

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.