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Comptes Rendus Mathématique
Volume 354, n° 11
pages 1065-1070 (novembre 2016)
Doi : 10.1016/j.crma.2016.09.008
Received : 12 August 2016 ;  accepted : 20 September 2016
Fekete–Szegö inequality for certain spiral-like functions
Inégalité de Fekete–Szegö pour certaines fonctions spiralées
 

Allu Vasudevarao
 Department of Mathematics, Indian Institute of Technology Khargpur, Kharagpur-721 302, West Bengal, India 

Abstract

For  , let   denote the class of non-vanishing normalized analytic functions   in the unit disk   satisfying   in   where
Pf(z)=eiα(1+zf″(z)f′(z)). The class   consists of functions   for which   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   for the complex parameter λ when  .

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Résumé

Pour  , soit   la classe des fonctions analytiques normalisées  , non nulles dans le disque unité   et satisfaisant   dans  , où
Pf(z)=eiα(1+zf″(z)f′(z)). Pour  , la fonction   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  , où λ est un paramètre complexe et  .

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