Comptes Rendus
Complex analysis
Second Hankel determinant for close-to-convex functions
[Deuxième déterminant de Hankel pour les fonctions presque convexes]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1063-1071.

Aucune estimation précise de l'expression |a2a4a32| pour la classe C des fonctions presque convexes n'était connue jusqu'à présent. Dans cette Note, nous présentons des estimations de cette expression, nommée deuxième déterminant de Hankel pour la classe C0, c'est-à-dire la sous-classe C, composée des fonctions f qui vérifient, dans le disque unité, l'inégalité Re(zf(z)/g(z))>0 avec une fonction étoilée g.

De plus, nous formulons quelques remarques à propos du deuxième déterminant de Hankel pour la classe S des fonctions univalentes. Nous démontrons que max{|a2a4a32|:fS} est plus grand que 1.

So far, the sharp bound of the expression |a2a4a32| for the class C of close-to-convex functions has remained unknown. In this paper, we obtain the estimation of this expression, called the second Hankel determinant, for C0, i.e. the subset of C consisting of functions f that satisfy in the unit disk the inequality Re(zf(z)/g(z))>0 with a starlike function g.

Moreover, some remarks on the second Hankel determinant for the class S of univalent functions are made. It is proven that max{|a2a4a32|:fS} is greater than 1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.006

Dorina Răducanu 1 ; Paweł Zaprawa 2

1 Faculty of Mathematics and Computer Science, Transilvania University of Braşov, Iuliu Maniu 50, 500091 Braşov, Romania
2 Faculty of Mechanical Engineering, Department of Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland
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Dorina Răducanu; Paweł Zaprawa. Second Hankel determinant for close-to-convex functions. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1063-1071. doi : 10.1016/j.crma.2017.09.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.006/

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