Volume 35, Issue 4
Some Estimates of the Maximum Modulus for Polynomials with Gaps

Anal. Theory Appl., 35 (2019), pp. 421-426.

Published online: 2020-01

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• Abstract

Let $p(z)$ be a polynomial of degree $n$ having some zeros at a point $z_0\in\mathbb{C}$ with $|z_0|<1$ and the rest of the zeros lying on or outside the boundary of a prescribed disk. In this brief note, we consider this class of polynomials and obtain some bounds for $\left(\max_{|z|=R}|p(z)|\right)^s$ in terms of $\left(\max_{|z|=1}|p(z)|\right)^s$ for any $R\geq 1$ and $s\in\mathbb{N}.$

• Keywords

Polynomials, maximum modulus, zeros, prescribed disk.

30C10, 30C80, 30D15, 26C10, 26D10

enwaeze@tuskegee.edu (Eze R. Nwaeze)

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@Article{ATA-35-421, author = {Eze R. and Nwaeze and enwaeze@tuskegee.edu and 6446 and Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA and Eze R. Nwaeze}, title = {Some Estimates of the Maximum Modulus for Polynomials with Gaps}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {35}, number = {4}, pages = {421--426}, abstract = {

Let $p(z)$ be a polynomial of degree $n$ having some zeros at a point $z_0\in\mathbb{C}$ with $|z_0|<1$ and the rest of the zeros lying on or outside the boundary of a prescribed disk. In this brief note, we consider this class of polynomials and obtain some bounds for $\left(\max_{|z|=R}|p(z)|\right)^s$ in terms of $\left(\max_{|z|=1}|p(z)|\right)^s$ for any $R\geq 1$ and $s\in\mathbb{N}.$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2018-0017}, url = {http://global-sci.org/intro/article_detail/ata/13621.html} }
TY - JOUR T1 - Some Estimates of the Maximum Modulus for Polynomials with Gaps AU - Nwaeze , Eze R. JO - Analysis in Theory and Applications VL - 4 SP - 421 EP - 426 PY - 2020 DA - 2020/01 SN - 35 DO - http://doi.org/10.4208/ata.OA-2018-0017 UR - https://global-sci.org/intro/article_detail/ata/13621.html KW - Polynomials, maximum modulus, zeros, prescribed disk. AB -

Let $p(z)$ be a polynomial of degree $n$ having some zeros at a point $z_0\in\mathbb{C}$ with $|z_0|<1$ and the rest of the zeros lying on or outside the boundary of a prescribed disk. In this brief note, we consider this class of polynomials and obtain some bounds for $\left(\max_{|z|=R}|p(z)|\right)^s$ in terms of $\left(\max_{|z|=1}|p(z)|\right)^s$ for any $R\geq 1$ and $s\in\mathbb{N}.$

Eze R. Nwaeze. (2020). Some Estimates of the Maximum Modulus for Polynomials with Gaps. Analysis in Theory and Applications. 35 (4). 421-426. doi:10.4208/ata.OA-2018-0017
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