TY - JOUR
T1 - Some Results on the Polar Derivative of a Polynomial
AU - A. Mir & B. Dar
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 - <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 $P(z)$ 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.</p>