Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions

Serap Bulut; Nanjundan Magesh; Vittalrao Kupparao Balaji

doi:10.1016/j.crma.2014.10.019

Complex analysis

Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions
[Estimations à l'aide des polynômes de Faber des coefficients de certaines fonctions méromorphes bi-univalentes]

Présenté par : the Editorial Board

Serap Bulut ¹ ; Nanjundan Magesh ² ; Vittalrao Kupparao Balaji ³

¹ Kocaeli University, Civil Aviation College, Arslanbey Campus, TR-41285 İzmit-Kocaeli, Turkey
² Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri 635001, Tamilnadu, India
³ Department of Mathematics, L.N. Govt College, Ponneri, Chennai, Tamilnadu, India

Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 113-116.

Résumé
Abstract

Utilisant les développements des coefficients en termes de polynômes de Faber, nous obtenons des estimations du coefficient général des éléments d'une classe de fonctions méromorphes bi-univalentes. Nous étudions aussi les bornes pour leurs coefficients initiaux. Les bornes présentées ici sont nouvelles dans leur genre.

Making use of the Faber polynomial coefficient expansions to a class of meromorphic bi-univalent functions, we obtain the general coefficient estimates for such functions and study their initial coefficient bounds. The coefficient bounds presented here are new in their own kind.

Reçu le : 2013-11-27
Accepté le : 2014-10-23
Publié le : 2014-11-24

DOI : 10.1016/j.crma.2014.10.019

Affiliations des auteurs :

Serap Bulut ¹ ; Nanjundan Magesh ² ; Vittalrao Kupparao Balaji ³

¹ Kocaeli University, Civil Aviation College, Arslanbey Campus, TR-41285 İzmit-Kocaeli, Turkey
² Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri 635001, Tamilnadu, India
³ Department of Mathematics, L.N. Govt College, Ponneri, Chennai, Tamilnadu, India

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     journal = {Comptes Rendus. Math\'ematique},
     pages = {113--116},
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Serap Bulut; Nanjundan Magesh; Vittalrao Kupparao Balaji. Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 113-116. doi : 10.1016/j.crma.2014.10.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.019/

Bibliographie
Cité par

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

[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

[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

[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

[5] S. Bulut Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math., Volume 43 (2013) no. 2, pp. 59-65

[6] S. Bulut Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014) no. 6, pp. 479-484

[7] M. Çağlar; H. Orhan; N. Yağmur Coefficient bounds for new subclasses of bi-univalent functions, Filomat, Volume 27 (2013) no. 7, pp. 1165-1171

[8] P.L. Duren Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983

[9] G. Faber Über polynomische Entwickelungen, Math. Ann., Volume 57 (1903) no. 3, pp. 389-408

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

[11] S. Gong The Bieberbach Conjecture, AMS/IP Studies in Advanced Mathematics, vol. 12, Amer. Math. Soc., Providence, RI, USA, 1999 (translated from the 1989 Chinese original and revised by the author)

[12] S.G. Hamidi; S.A. Halim; J.M. Jahangiri Coefficient estimates for a class of meromorphic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013) no. 9–10, pp. 349-352

[13] S.G. Hamidi; S.A. Halim; J.M. Jahangiri Faber polynomial coefficient estimates for meromorphic bi-starlike functions, Int. J. Math. Math. Sci., Volume 2013 (2013) (Art. ID 498159, 4 p)

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

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

[16] E. Netanyahu The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $| z | < 1$ , Arch. Ration. Mech. Anal., Volume 32 (1969), pp. 100-112

[17] H. Orhan, N. Magesh, V.K. Balaji, Initial coefficient bounds for certain classes of meromorphic bi-univalent functions, preprint.

[18] H.M. Srivastava; S. Bulut; M. Çağlar; N. Yağmur Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, Volume 27 (2013) no. 5, pp. 831-842

[19] 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

[20] 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

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