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} }