Inequalities for the polar derivative of a polynomial

Abstract

Let $P(z)$ be a polynomial of degree $n$ and for any real or complex number $\alpha ,$ let $D_{\alpha }P(z)=nP(z)+(\alpha -z)P^{\prime }(z)$ denote the polar derivative with respect to $\alpha .$ In this paper, we obtain generalizations of some inequalities for the polar derivative of a polynomial.

14 pages