Some Results on the Polar Derivative of a Polynomial (Analysis in Theory and Applications, 2014)
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 $P(z)$ 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.