TY - JOUR T1 - Maximum Modulus of Polynomials JO - Analysis in Theory and Applications VL - 2 SP - 110 EP - 117 PY - 2017 DA - 2017/05 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n2.2 UR - https://global-sci.org/intro/article_detail/ata/10039.html KW - Maximum modulus, growth of polynomial, derivative. AB -

Let $$P(z)= \sum_{j=0}^{n}a_j z^j$$ be a polynomial of degree $n$ and let $M(P,r)=\underset{|z|=r}{\max} |P(z)|$. If $P(z)\neq 0$ in $|z|<1$, then $$M(P,r)\geq {\bigg(\frac{1+r}{1+\rho}\bigg)^n}M(P,\rho).$$The result is best possible. In this paper we shall present a refinement of this result and some other related results.