TY - JOUR
T1 - On Growth of Polynomials with Restricted Zeros
AU - Abdullah Mir , 
AU - G. N. Parrey , 
JO - Analysis in Theory and Applications
VL - 2
SP - 181
EP - 188
PY - 2016
DA - 2016/04
SN - 32
DO - http://doi.org/10.4208/ata.2016.v32.n2.7
UR - https://global-sci.org/intro/article_detail/ata/4664.html
KW - Polynomial, maximum modulus principle, zeros.
AB - <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>