no. 4
Complex analysis
Faber polynomial coefficients of bi-subordinate functions
[Polynômes de Faber et coefficients des fonctions bi-subordonnées]

Présenté par : Jean-Pierre Demailly

Hamidi, Samaneh G.1 ; Jahangiri, Jay M.2
1 Department of Mathematics, Brigham Young University, Provo, UT 84604, USA
2 Department of Mathematical Sciences, Kent State University, Burton, OH 44021, USA
Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 365-370.

Une fonction est dite bi-univalente dans le disque unité ouvert D si elle et son inverse sont univalentes dans D. Dans le même ordre, une fonction est dite bi-subordonnée dans D si elle et son inverse sont subordonnées à une fonction donnée dans D. Le comportement des coefficients de telles fonctions est imprévisible et inconnu. Dans cette Note, nous utilisons les développements en polynômes de Faber afin d'établir une borne supérieure pour le ne (n≥3) coefficient d'une fonction bi-subordonnée, lorsque les n−2 précédents coefficients sont nuls. Nous donnons également des bornes plus précises pour les deux premiers coefficients de telles fonctions.

A function is said to be bi-univalent in the open unit disk D if both the function and its inverse map are univalent in D. By the same token, a function is said to be bi-subordinate in D if both the function and its inverse map are subordinate to certain given function in D. The behavior of the coefficients of such functions are unpredictable and unknown. In this paper, we use the Faber polynomial expansions to find upper bounds for the n-th (n≥3) coefficients of classes of bi-subordinate functions subject to a gap series condition as well as determining bounds for the first two coefficients of such functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.01.013
Hamidi, Samaneh G. 1 ; Jahangiri, Jay M. 2

1 Department of Mathematics, Brigham Young University, Provo, UT 84604, USA
2 Department of Mathematical Sciences, Kent State University, Burton, OH 44021, USA 
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Hamidi, Samaneh G.; Jahangiri, Jay M. Faber polynomial coefficients of bi-subordinate functions. Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 365-370. doi : 10.1016/j.crma.2016.01.013. http://www.numdam.org/articles/10.1016/j.crma.2016.01.013/

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