IJPAM: Volume 13, No. 4 (2004)

GROWTH OF POLYNOMIALS NOT VANISHING
INSIDE A CIRCLE

Robert B. Gardner$^1$, N.K. Govil$^2$, Amy Weems$^3$
$^{1,3}$Department of Mathematics
East Tennessee State University
Johnson City, TN 37614, USA
$^1$e-mail: gardnerr@etsu.edu
$^2$Department of Mathematics
College of Science and Mathematics
Auburn University
218 Parker Hall, Auburn, AL 36849-5310, USA
e-mail: govilnk@auburn.edu


Abstract.A well-known theorem of Ankeny and Rivlin states that if $\pz$ is a polynomial of degree $n$, $\pz \ne 0$ for $\vert z\vert<1$, then $\max \limits_{\vert z\vert=R>1}\vert\pz\vert \le (\frac{R^n+1}{2}) \Mx \vert\pz\vert$. In this paper we generalize and sharpen this, and some other results in this direction.

Received: March 24, 2004

AMS Subject Classification: 30A10, 30C10, 30E10, 30C15

Key Words and Phrases: polynomials, restricted zeros, growth, inequalities

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 4