Year: 2016
Author: Abdullah Mir, G. N. Parrey
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 2 : pp. 181–188
Abstract
Let $P(z)$ be a polynomial of degree $n$ which does not vanish in $|z|< k $, $k\geq 1$. It is known that for each $0\leq s< n$ 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 $P(z)$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n2.7
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 2 : pp. 181–188
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Polynomial maximum modulus principle zeros.