Maximum Modulus of Polynomials

Maximum Modulus of Polynomials

Year:    2017

Analysis in Theory and Applications, Vol. 33 (2017), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2017.v33.n2.2

Analysis in Theory and Applications, Vol. 33 (2017), Iss. 2 : pp. 110–117

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Maximum modulus growth of polynomial derivative.