On the Polar Derivative of A Polynomial

Let P(z) be a polynomial of degree n and for any complex number α, let D_α P(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 certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.