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 - <p style="text-align: justify;">Let $p(z)$ be a polynomial of degree $n$ having some zeros at a point $z_0\in\mathbb{C}$ with $|z_0|&lt;1$ 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 $s\in\mathbb{N}.$</p>