TY - JOUR T1 - On an Inequality of Paul Turan Concerning Polynomials-II JO - Analysis in Theory and Applications VL - 3 SP - 236 EP - 243 PY - 2017 DA - 2017/07 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n3.2 UR - https://global-sci.org/intro/article_detail/ata/4636.html KW - Polar derivative, polynomials, inequalities, maximum modulus, growth. AB -

Let $P(z)$ be a polynomial of degree $n$ and for any complex number $\alpha$, let $D_{\alpha}P(z)=nP(z)+(\alpha-z)P'(z)$ denote the polar derivative of the polynomial $P(z)$ with respect to $\alpha$. 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.