Copyright © 2009 M. Bidkham et al. 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) be a polynomial of degree n and for any real or complex number α, and let Dαp(z)=np(z)+(α−z)p′(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain new results concerning the maximum modulus of a polar derivative of a polynomial with restricted zeros. Our results generalize as well as improve upon some well-known polynomial inequalities.