Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 515709, 9 pages
Research Article

Inequalities for the Polar Derivative of a Polynomial

Department of Mathematics, Faculty of Natural Sciences, Semnan University, Semnan 35195-363, Iran

Received 11 August 2009; Accepted 30 November 2009

Academic Editor: Narendra Kumar Govil

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.


Let p(z) be a polynomial of degree n and for any real or complex number α, and let Dαp(z)=np(z)+(αz)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.