×

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.) (English. French summary) Zbl 1308.30031

Summary: 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.

MSC:

30D30 Meromorphic functions of one complex variable (general theory)
30C10 Polynomials and rational functions of one complex variable
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
Full Text: DOI

References:

[1] Airault, H.; Bouali, A., Differential calculus on the Faber polynomials, Bull. Sci. Math., 130, 3, 179-222 (2006) · Zbl 1163.30301
[2] Airault, H.; Ren, J., An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126, 5, 343-367 (2002) · Zbl 1010.33006
[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., 25, 3, 344-351 (2012) · Zbl 1246.30018
[4] Brannan, D. A.; Taha, T. S., On some classes of bi-univalent functions, Stud. Univ. Babeş-Bolyai, Math., 31, 2, 70-77 (1986) · Zbl 0614.30017
[5] Bulut, S., Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math., 43, 2, 59-65 (2013) · Zbl 1349.30040
[6] Bulut, S., Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 352, 6, 479-484 (2014) · Zbl 1300.30017
[7] Çağlar, M.; Orhan, H.; Yağmur, N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat, 27, 7, 1165-1171 (2013) · Zbl 1324.30017
[8] Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259 (1983), Springer: Springer New York · Zbl 0514.30001
[9] Faber, G., Über polynomische Entwickelungen, Math. Ann., 57, 3, 389-408 (1903) · JFM 34.0430.01
[10] Frasin, B. A.; Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett., 24, 9, 1569-1573 (2011) · Zbl 1218.30024
[11] Gong, S., The Bieberbach Conjecture, AMS/IP Studies in Advanced Mathematics, vol. 12 (1999), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI, USA, translated from the 1989 Chinese original and revised by the author · Zbl 0931.30009
[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, 351, 9-10, 349-352 (2013) · Zbl 1283.30026
[13] Hamidi, S. G.; Halim, S. A.; Jahangiri, J. M., Faber polynomial coefficient estimates for meromorphic bi-starlike functions, Int. J. Math. Math. Sci., 2013 (2013), Art. ID 498159, 4 p · Zbl 1263.30005
[14] Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18, 63-68 (1967) · Zbl 0158.07802
[15] Löwner, K., Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann., 89, 1-2, 103-121 (1923) · JFM 49.0714.01
[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., 32, 100-112 (1969) · Zbl 0186.39703
[18] Srivastava, H. M.; Bulut, S.; Çağlar, M.; Yağmur, N., Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27, 5, 831-842 (2013) · Zbl 1432.30014
[19] Srivastava, H. M.; Mishra, A. K.; Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23, 10, 1188-1192 (2010) · Zbl 1201.30020
[20] Todorov, P. G., On the Faber polynomials of the univalent functions of class \(Σ\), J. Math. Anal. Appl., 162, 1, 268-276 (1991) · Zbl 0752.30002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.