TY - JOUR T1 - Some Results on the Polar Derivative of a Polynomial JO - Analysis in Theory and Applications VL - 3 SP - 306 EP - 317 PY - 2014 DA - 2014/10 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n3.7 UR - https://global-sci.org/intro/article_detail/ata/4495.html KW - Polynomial, zeros, polar derivative, Bernstein inequality. 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 $P(z)$ with respect to $\alpha$. 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.