Geodesic
Entire functions of exponential type not vanishing in the half-plane \(\Im z > k\), where \(k > 0\)
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1.

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Let P (z) be a polynomial of degree n having no zeros in |z| lt; k, k ≤ 1, and let Q (z) := z^n P (1/z). It was shown by Govil that if max_|z| = 1 |P^' (z)| and max_|z| = 1 |Q^' (z)| are attained at the same point of the unit circle |z| = 1, then max_|z| = 1 |P'(z)| ≤n/1 + k^nmax_|z| = 1 |P(z)|. The main result of the present article is a generalization of Govil's polynomial inequality to a class of entire functions of exponential type.
Keywords: Inequalities, entire functions of exponential type, polynomial, trigonometric polynomial 
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Hachani, Mohamed Amine. Entire functions of exponential type not vanishing in the half-plane \(\Im z > k\), where \(k > 0\). Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1. http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a3/

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