Some Results on the Polar Derivative of a Polynomial

摘要

Let P(z) be a polynomial of degree n and for any complex number α, let Dα P(z) = n P(z)+(α-z)P′(z) denote the polar derivative of P(z) with respect to α. 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.