Advances on the coefficients of bi-prestarlike functions

Jay M. Jahangiri; Samaneh G. Hamidi

doi:10.1016/j.crma.2016.08.009

Complex analysis

Advances on the coefficients of bi-prestarlike functions

Presented by: the Editorial Board

Jay M. Jahangiri ¹; Samaneh G. Hamidi ²

¹ Department of Mathematical Sciences, Kent State University, Burton, OH 44021-9500, USA
² Department of Mathematics, Brigham Young University, Provo, UT 84604, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 980-985.

Abstract
Résumé

Since 1923, when Löwner proved that the inverse of the Koebe function provides the best upper bound for the coefficients of the inverses of univalent functions, finding sharp bounds for the coefficients of the inverses of subclasses of univalent functions turned out to be a challenge. Coefficient estimates for the inverses of such functions proved to be even more involved under the bi-univalency requirement. In this paper, we use the Faber polynomial expansions to find upper bounds for the coefficients of bi-prestarlike functions and consequently advance some of the previously known estimates.

Depuis 1923, lorsque Löwner a montré que l'inverse de la fonction de Koebe fournit la majoration optimale pour les coefficients des inverses des fonctions univalentes, s'est posé le défi de trouver des bornes fines pour les coefficients des inverses de fonctions univalentes dans certaines classes. Ce problème s'est révélé être encore plus intriqué sous la condition de bi-univalence. Utilisant les développements de polynômes de Faber pour les coefficients des fonctions bi-pré-étoilées, nous améliorons dans cette Note quelques estimations déjà connues.

Received: 2016-06-01
Accepted: 2016-08-08
Published online: 2016-09-12

DOI: 10.1016/j.crma.2016.08.009

Author's affiliations:

Jay M. Jahangiri ¹; Samaneh G. Hamidi ²

¹ Department of Mathematical Sciences, Kent State University, Burton, OH 44021-9500, USA
² Department of Mathematics, Brigham Young University, Provo, UT 84604, USA

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Jay M. Jahangiri; Samaneh G. Hamidi. Advances on the coefficients of bi-prestarlike functions. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 980-985. doi : 10.1016/j.crma.2016.08.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.08.009/

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