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Proceedings of the American Mathematical Society

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Inequalities for polynomials satisfying $ p(z)\equiv z\sp{n}p(1/z)$


Authors: N. K. Govil, V. K. Jain and G. Labelle
Journal: Proc. Amer. Math. Soc. 57 (1976), 238-242
MSC: Primary 30A06
DOI: https://doi.org/10.1090/S0002-9939-1976-0414838-4
MathSciNet review: 0414838
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Abstract: If $ p(z) = \Sigma_{v = 0}^n {{a_v}} {z^v}$ is a polynomial of degree $ n$, then it is known that $ {\operatorname{Max} _{\vert z\vert = 1}}\vert p'(z)\vert \leq n{\operatorname{Max} _{\vert z\vert = 1}}\vert p(z)\vert$. In this paper we obtain the analogous inequality for a subclass of polynomials satisfying $ p(z) \equiv {z^n}p(1/z)$. Some other inequalities have also been obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0414838-4
Keywords: Inequalities in complex domain, polynomials, extremal problems
Article copyright: © Copyright 1976 American Mathematical Society

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