Inequalities for polynomials satisfying 𝑝(𝑧)≡𝑧ⁿ𝑝(1/𝑧)

Govil, N. K.; Jain, V. K.; Labelle, G.

doi:10.1090/S0002-9939-1976-0414838-4

Inequalities for polynomials satisfying $p(z)\equiv z^{n}p(1/z)$
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by N. K. Govil, V. K. Jain and G. Labelle PDF

Proc. Amer. Math. Soc. 57 (1976), 238-242 Request permission

Abstract:

If $p(z) = \Sigma _{v = 0}^n {{a_v}} {z^v}$ is a polynomial of degree $n$, then it is known that ${\operatorname {Max} _{|z| = 1}}|p’(z)| \leq n{\operatorname {Max} _{|z| = 1}}|p(z)|$. 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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