Comptes Rendus
Complex analysis
Faber polynomial coefficients of bi-subordinate functions
Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 365-370.

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 (n3) 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.

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 (n3) coefficient d'une fonction bi-subordonnée, lorsque les n2 précédents coefficients sont nuls. Nous donnons également des bornes plus précises pour les deux premiers coefficients de telles fonctions.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.013

Samaneh G. Hamidi 1; Jay M. Jahangiri 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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Samaneh G. Hamidi; Jay M. Jahangiri. Faber polynomial coefficients of bi-subordinate functions. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 365-370. doi : 10.1016/j.crma.2016.01.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.013/

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