Comptes Rendus
Complex Analysis
Coefficient estimates for a class of meromorphic bi-univalent functions
[Estimation de coefficients pour une classe de fonctions méromorphes bi-univalentes]
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 349-352.

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.

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.

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Accepté le :
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DOI : 10.1016/j.crma.2013.05.005

Samaneh G. Hamidi 1 ; Suzeini A. Halim 1 ; Jay M. Jahangiri 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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Samaneh G. Hamidi; Suzeini A. Halim; Jay M. Jahangiri. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.05.005/

[1] H. Airault; A. Bouali Differential calculus on the Faber polynomials, Bull. Sci. Math., Volume 130 (2006) no. 3, pp. 179-222 MR2215663 (2007e:30002)

[2] H. Airault; J. Ren An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., Volume 126 (2002) no. 5, pp. 343-367 MR1914725 (2004c:17048)

[3] R.M. Ali; S.K. Lee; V. Ravichandran; S. Supramaniam Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett., Volume 25 (2012) no. 3, pp. 344-351 MR2855984 (2012h:30105)

[4] D.A. Brannan; T.S. Taha On some classes of bi-univalent functions, Stud. Univ. Babeş-Bolyai, Math., Volume 31 (1986) no. 2, pp. 70-77 MR0911858 (88k:30012)

[5] P.L. Duren Univalent Functions, Grundlehren Math. Wiss., vol. 259, Springer, New York, 1983 MR0708494 (85j:30034)

[6] B.A. Frasin; M.K. Aouf New subclasses of bi-univalent functions, Appl. Math. Lett., Volume 24 (2011) no. 9, pp. 1569-1573 MR2803711 (2012j:30027)

[7] J.G. Krzyż; R.J. Libera; E. Złotkiewicz Coefficients of inverses of regular starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A, Volume 33 (1979), pp. 103-110 MR0689590 (84d:30027)

[8] M. Lewin On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., Volume 18 (1967), pp. 63-68 MR0206255 (34 #6074)

[9] K. Lowner Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann., Volume 89 (1923) no. 1–2, pp. 103-121 (MR1512136)

[10] H.M. Srivastava; A.K. Mishra; P. Gochhayat Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., Volume 23 (2010) no. 10, pp. 1188-1192 MR2665593 (2011e:30055)

[11] P.G. Todorov On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., Volume 162 (1991) no. 1, pp. 268-276 MR1135277 (93d:30023)

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