[Bornes des coefficients des développements en polynômes de Faber d'une sous-classe de fonctions bi-univalentes]
Dans cet article, on considère une sous-classe de fonctions bi-univalentes ; en utilisant les développements en polynômes de Faber, on obtient les coefficients de ces développements pour les fonctions de la sous-classe considérée. Dans certains cas, les estimations sur les bornes des coefficients améliorent des résultats déjà connus.
In this work, considering a general subclass of bi-univalent functions and using the Faber polynomials, we obtain coefficient expansions for functions in this class. In certain cases, our estimates improve some of those existing coefficient bounds.
Accepté le :
Publié le :
@article{CRMATH_2015__353_12_1075_0,
author = {Alt{\i}nkaya, \c{S}ahsene and Yal\c{c}{\i}n, Sibel},
title = {Faber polynomial coefficient bounds for a subclass of bi-univalent functions},
journal = {Comptes Rendus. Math\'ematique},
pages = {1075--1080},
publisher = {Elsevier},
volume = {353},
number = {12},
year = {2015},
doi = {10.1016/j.crma.2015.09.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.09.003/}
}
TY - JOUR AU - Altınkaya, Şahsene AU - Yalçın, Sibel TI - Faber polynomial coefficient bounds for a subclass of bi-univalent functions JO - Comptes Rendus. Mathématique PY - 2015 SP - 1075 EP - 1080 VL - 353 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.09.003/ DO - 10.1016/j.crma.2015.09.003 LA - en ID - CRMATH_2015__353_12_1075_0 ER -
%0 Journal Article %A Altınkaya, Şahsene %A Yalçın, Sibel %T Faber polynomial coefficient bounds for a subclass of bi-univalent functions %J Comptes Rendus. Mathématique %D 2015 %P 1075-1080 %V 353 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.09.003/ %R 10.1016/j.crma.2015.09.003 %G en %F CRMATH_2015__353_12_1075_0
Altınkaya, Şahsene; Yalçın, Sibel. Faber polynomial coefficient bounds for a subclass of bi-univalent functions. Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1075-1080. doi : 10.1016/j.crma.2015.09.003. http://www.numdam.org/articles/10.1016/j.crma.2015.09.003/
[1] Symmetric sums associated to the factorization of Grunsky coefficients, Montreal, Canada (April 2007)
[2] Remarks on Faber polynomials, Int. Math. Forum, Volume 3 (2008) no. 9, pp. 449-456
[3] Differential calculus on the Faber polynomials, Bull. Sci. Math., Volume 130 (2006) no. 3, pp. 179-222
[4] 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
[5] Initial coefficient bounds for a general class of bi-univalent functions, Int. J. Anal. (2014)
[6] Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math., Volume 6 (2015) no. 2, pp. 180-185
[7] Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Institute Held at University of Durham, Academic Press, New York, 1979
[8] On some classes of bi-univalent functions, Stud. Univ. Babeş–Bolyai, Math., Volume 31 (1986) no. 2, pp. 70-77
[9] Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I (2015) (in press)
[10] Coefficient estimates certain subclasses of bi-univalent functions, Gen. Math. Notes, Volume 16 (2013) no. 2, pp. 93-1002
[11] (Grundlehren Math. Wiss.), Springer, New York, USA (1983), p. 259
[12] Über polynomische Entwickelungen, Math. Ann., Volume 57 (1903) no. 3, pp. 1569-1573
[13] New subclasses of bi-univalent functions, Appl. Math. Lett., Volume 24 (2011), pp. 1569-1573
[14] Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen, Math. Z., Volume 45 (1939), pp. 29-61
[15] Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014) no. 1, pp. 17-20
[16] Faber polynomial coefficient estimates for meromorphic bi-starlike functions, Int. J. Math. Math. Sci. (2013)
[17] Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci. (2013) (190560)
[18] Coefficient inequality for certain new subclasses of analytic bi-univalent functions, Theor. Math. Appl., Volume 3 (2013) no. 1, pp. 1-10
[19] On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., Volume 18 (1967), pp. 63-68
[20] Two new subclasses of bi-univalent functions, Int. Math. Forum, Volume 7 (2012), pp. 1495-1504
[21] Coefficient bounds for a certain subclass of bi-univalent functions, Int. Math. Forum, Volume 8 (2013) no. 27, pp. 1337-1344
[22] The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in , Arch. Ration. Mech. Anal., Volume 32 (1969), pp. 100-112
[23] On a new subclass of bi-univalent functions, J. Egypt. Math. Soc., Volume 21 (2013) no. 3, pp. 190-193
[24] Subclasses of Univalent Functions, Fifth Romanian Finish Seminar, Bucharest (1983), pp. 362-372
[25] The coefficients of schlicht functions, Duke Math. J., Volume 10 (1943), pp. 611-635
[26] A method of variation within the family of simple functions, Proc. Lond. Math. Soc., Volume 44 (1938) no. 2, pp. 432-449
[27] Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., Volume 23 (2010) no. 10, pp. 1188-1192
[28] Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, Volume 27 (2013) no. 5, pp. 831-842
[29] Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., Volume 25 (2012), pp. 990-994
Cité par Sources :
