… EXTENSION OF SOME POLYNOMIAL INEQUALITIES TO THE POLAR DERIVATIVE …
In this paper, we extend the above inequality to the class of polynomials P(z) = anzn +∑ n …

Let p (z) be a polynomial of degree n and for any real or complex number α, 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 inequalities for the polar derivative of a polynomial having all its zeros
inside or outside a circle. Our results shall generalize and sharpen some well-known
polynomial inequalities.