On the Polar Derivative of a Polynomial

Abstract

Let P(z) be a polynomial of degree n and for any complex number a, let Da P(z) = n P(z)+(a -z)P'(z) denote the polar derivative of the polynomial P(z) with respect to a. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.