On Growth of Polynomials with Restricted Zeros

On Growth of Polynomials with Restricted Zeros

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.

Author Details

Abdullah Mir

G. N. Parrey