On the inequality |𝑝(𝑧)|≤𝑝(|𝑧|) for polynomials

De Angelis, Valerio

doi:10.1090/S0002-9939-1995-1264805-8

On the inequality $\vert p(z)\vert \leq p(\vert z\vert )$ for polynomials
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Proc. Amer. Math. Soc. 123 (1995), 2999-3007 Request permission

Abstract:

We derive a simple test to check if the inequality $|p(z)| \leq p(|z|)$ holds for all sufficiently small or sufficiently large values of $|z|$, where p is a Laurent polynomial in one variable with real coefficients and $z \in \mathbb {C}$. Some examples and applications are also given.

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