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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the inequality $ \vert p(z)\vert \leq p(\vert z\vert )$ for polynomials


Author: Valerio De Angelis
Journal: Proc. Amer. Math. Soc. 123 (1995), 2999-3007
MSC: Primary 26C05; Secondary 26D05, 30C10
MathSciNet review: 1264805
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Abstract: We derive a simple test to check if the inequality $ \vert p(z)\vert \leq p(\vert z\vert)$ holds for all sufficiently small or sufficiently large values of $ \vert z\vert$, 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1264805-8
PII: S 0002-9939(1995)1264805-8
Article copyright: © Copyright 1995 American Mathematical Society