Volume 33, Issue 2
Maximum Modulus of Polynomials

B. A. Zargar and B. Shaista

10.4208/ata.2017.v33.n2.2

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

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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 relatedresults.

  • History

Published online: 2017-05

  • AMS Subject Headings

30A10, 30C10, 30C15

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