On an Inequality of Paul Turan Concerning Polynomials-II (Analysis in Theory and Applications, 2017)
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 inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.