Entire functions of exponential type not vanishing in the half-plane Iz>k, where k>0

Abstract

Let P(z) be a polynomial of degree n having no zeros in |z|<k, k≤1, and let Q(z):=znP(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+kn)max|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.

Authors and Affiliations

Mohamed Hachani

Keywords

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  • EP ID EP304586
  • DOI 10.17951/a.2017.71.1.31
  • Views 109
  • Downloads 0

How To Cite

Mohamed Hachani (2017). Entire functions of exponential type not vanishing in the half-plane Iz>k, where k>0. Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica, 71(1), 31-39. https://europub.co.uk/articles/-A-304586