Complex analysis
Fekete–Szegö inequality for certain spiral-like functions
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1065-1070.

For |α|<π/2, let Sα denote the class of non-vanishing normalized analytic functions f(z)=z+n=2anzn in the unit disk D:={zC:|z|<1} satisfying RePf(z)>0 in D where

Pf(z)=eiα(1+zf(z)f(z)).
The class Sα consists of functions f(z) for which zf(z) is spiral-like, which has been introduced and extensively studied by M.S. Robertson [24]. In the present paper, we obtain the sharp upper bound for the Fekete–Szegö functional |a3λa22| for the complex parameter λ when fSα.

Pour |α|<π/2, soit Sα la classe des fonctions analytiques normalisées f(z)=z+n=2anzn, non nulles dans le disque unité D:={zC;|z|<1} et satisfaisant RePf(z)>0 dans D, où

Pf(z)=eiα(1+zf(z)f(z)).
Pour f(z)Sα, la fonction zf(z) est spiralée, notion introduite et étudiée de façon approfondie par M.S. Robertson [24]. Dans la présente Note, nous obtenons une borne supérieure précise de la fonctionnelle de Fekete–Szegö |a3λa22|, où λ est un paramètre complexe et fSα.

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DOI: 10.1016/j.crma.2016.09.008
Vasudevarao, Allu 1

1 Department of Mathematics, Indian Institute of Technology Khargpur, Kharagpur-721 302, West Bengal, India
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Vasudevarao, Allu. Fekete–Szegö inequality for certain spiral-like functions. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1065-1070. doi : 10.1016/j.crma.2016.09.008. http://www.numdam.org/articles/10.1016/j.crma.2016.09.008/

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