Volume 33, Issue 2
Maximum Modulus of Polynomials

Anal. Theory Appl., 33 (2017), pp. 110-117.

Published online: 2017-05

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• Abstract

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.

• AMS Subject Headings

30A10, 30C10, 30C15

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@Article{ATA-33-110, author = {}, title = {Maximum Modulus of Polynomials}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {2}, pages = {110--117}, abstract = {

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} }
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.

B. A. Zargar & B. Shaista. (1970). Maximum Modulus of Polynomials. Analysis in Theory and Applications. 33 (2). 110-117. doi:10.4208/ata.2017.v33.n2.2
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