Complex Analysis
Coefficient estimates for a class of meromorphic bi-univalent functions
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 349-352.

Applying the Faber polynomial coefficient expansions to a class of meromorphic bi-univalent functions, we obtain the general coefficient estimates for such functions and also examine their early coefficient bounds. A function univalent in the open unit disk is said to be bi-univalent if its inverse map is also univalent there. Both the technique and the coefficient bounds presented here are new on their own kind. We hope that this article will generate future interest in applying our approach to other related problems.

Une fonction univalente dans le disque unité ouvert est dite bi-univalente si sa fonction inverse est aussi univalente dans ce domaine. Appliquant le développement à coefficients polynômes de Faber à cette classe de fonctions, nous obtenons des estimations du coefficient général de leur développement de Laurent. Nous examinons également les bornes pour leurs premiers coefficients. Les techniques et les bornes des coefficients présentées ici sont nouvelles dans leur genre. Nous espérons quʼelles susciteront un intérêt pour lʼapplication de notre approche à des problèmes connexes.

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DOI: 10.1016/j.crma.2013.05.005
Hamidi, Samaneh G. 1; Halim, Suzeini A. 1; Jahangiri, Jay M. 2

1 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
2 Department of Mathematical Sciences, Kent State University, Burton, OH 44021-9500, USA
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Hamidi, Samaneh G.; Halim, Suzeini A.; Jahangiri, Jay M. Coefficient estimates for a class of meromorphic bi-univalent functions. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 349-352. doi : 10.1016/j.crma.2013.05.005. http://www.numdam.org/articles/10.1016/j.crma.2013.05.005/

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