@Article{ATA-32-181,
author = {Abdullah Mir ,  and G. N. Parrey , },
title = {On Growth of Polynomials with Restricted Zeros},
journal = {Analysis in Theory and Applications},
year = {2016},
volume = {32},
number = {2},
pages = {181--188},
abstract = {<p style="text-align: justify;">Let $P(z)$ be a polynomial of degree $n$ which does not vanish in $|z|&lt; k $, $k\geq 1$. It is known that for each $0\leq s&lt; n$ and $1\leq R\leq k$, $$M\big(P^{(s)},R\big)\leq \Big(\frac{1}{R^{s}+k^{s}}\Big)\Big[\Big\{\frac{d^{(s)}}{dx^{(s)}}(1+x^{n})\Big\}_{x=1}\Big]\Big(\frac{R+k}{1+k}\Big)^{n}M(P,1).$$ In this paper, we obtain certain extensions and refinements of this inequality by involving binomial coefficients and some of the coefficients of the polynomial $P(z)$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2016.v32.n2.7},
url = {http://global-sci.org/intro/article_detail/ata/4664.html}
}