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

Bulut, Serap1 ; Magesh, Nanjundan2 ; Balaji, Vittalrao Kupparao3
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, Tome 353 (2015) no. 2, pp. 113-116.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.10.019
Bulut, Serap 1 ; Magesh, Nanjundan 2 ; Balaji, Vittalrao Kupparao 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 
@article{CRMATH_2015__353_2_113_0,
     author = {Bulut, Serap and Magesh, Nanjundan and Balaji, Vittalrao Kupparao},
     title = {Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {113--116},
     publisher = {Elsevier},
     volume = {353},
     number = {2},
     year = {2015},
     doi = {10.1016/j.crma.2014.10.019},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2014.10.019/}
}
TY  - JOUR
AU  - Bulut, Serap
AU  - Magesh, Nanjundan
AU  - Balaji, Vittalrao Kupparao
TI  - Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 113
EP  - 116
VL  - 353
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2014.10.019/
DO  - 10.1016/j.crma.2014.10.019
LA  - en
ID  - CRMATH_2015__353_2_113_0
ER  - 
%0 Journal Article
%A Bulut, Serap
%A Magesh, Nanjundan
%A Balaji, Vittalrao Kupparao
%T Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions
%J Comptes Rendus. Mathématique
%D 2015
%P 113-116
%V 353
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2014.10.019/
%R 10.1016/j.crma.2014.10.019
%G en
%F CRMATH_2015__353_2_113_0
Bulut, Serap; Magesh, Nanjundan; Balaji, Vittalrao Kupparao. Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions. Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 113-116. doi : 10.1016/j.crma.2014.10.019. http://www.numdam.org/articles/10.1016/j.crma.2014.10.019/

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cité par Sources :