Anal. Theory Appl., 33 (2017), pp. 110-117.
Published online: 2017-05
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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.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n2.2}, url = {http://global-sci.org/intro/article_detail/ata/10039.html} }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.