TY - JOUR
T1 - On an Inequality of Paul Turan Concerning Polynomials-II
AU - A. Mir
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 - <p style="text-align: justify;">Let $P(z)$ be a polynomial of degree $n$ and for any complex number $\alpha$, let $D_{\alpha}P(z)=nP(z)+(\alpha-z)P&#39;(z)$ 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.</p>