In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor–Maclaurin coefficients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.
Dans cette Note, nous considérons une sous-classe générale de fonctions analytiques bi-univalentes, pour lesquelles nous établissons des estimations du coefficient général de Taylor–Maclaurin. Nous utilisons à cet effet des développements en polynômes de Faber. Dans certains cas, nos estimations améliorent des bornes existantes sur les coefficients de ces fonctions.
Accepted:
Published online:
Serap Bulut 1
@article{CRMATH_2014__352_6_479_0, author = {Serap Bulut}, title = {Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions}, journal = {Comptes Rendus. Math\'ematique}, pages = {479--484}, publisher = {Elsevier}, volume = {352}, number = {6}, year = {2014}, doi = {10.1016/j.crma.2014.04.004}, language = {en}, }
TY - JOUR AU - Serap Bulut TI - Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions JO - Comptes Rendus. Mathématique PY - 2014 SP - 479 EP - 484 VL - 352 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2014.04.004 LA - en ID - CRMATH_2014__352_6_479_0 ER -
Serap Bulut. Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions. Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 479-484. doi : 10.1016/j.crma.2014.04.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.04.004/
[1] Differential calculus on the Faber polynomials, Bull. Sci. Math., Volume 130 (2006) no. 3, pp. 179-222
[2] New subclasses of biunivalent functions involving Dziok–Srivastava operator, ISRN Math. Anal. (2013) (Article ID 387178, 5 p)
[3] 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
[4] Durham, July 1–20, 1979 (1980)
[5] , Kuwait, February 18–21, 1985 (KFAS Proc. Ser.), Volume vol. 3 (1988) no. 2, pp. 53-60 (see also Stud. Univ. Babeş–Bolyai, Math., 31, 1986, pp. 70-77)
[6] Coefficient estimates for initial Taylor–Maclaurin coefficients for a subclass of analytic and bi-univalent functions defined by Al-Oboudi differential operator, Sci. World J. (2013) (Article ID 171039, 6 p)
[7] Coefficient estimates for new subclasses of analytic and bi-univalent functions defined by Al-Oboudi differential operator, J. Funct. Spaces Appl. (2013) (Article ID 181932, 7 p)
[8] S. Bulut, Coefficient estimates for a new subclass of analytic and bi-univalent functions, Ann. Alexandru Ioan Cuza Univ., Math., in press.
[9] Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math., Volume 43 (2013) no. 2, pp. 59-65
[10] Coefficient bounds for new subclasses of bi-univalent functions, Filomat, Volume 27 (2013) no. 7, pp. 1165-1171
[11] Univalent Functions, Grundlehren Math. Wiss., vol. 259, Springer, New York, 1983
[12] Über polynomische Entwickelungen, Math. Ann., Volume 57 (1903) no. 3, pp. 389-408
[13] New subclasses of bi-univalent functions, Appl. Math. Lett., Volume 24 (2011), pp. 1569-1573
[14] Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egypt. Math. Soc., Volume 20 (2012), pp. 179-182
[15] 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
[16] 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
[17] Coefficient estimates for certain classes of meromorphic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014) no. 4, pp. 277-282
[18] Coefficient bounds for bi-univalent functions, Panam. Math. J., Volume 22 (2012) no. 4, pp. 15-26
[19] Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci. (2013) (Article ID 190560, 4 p)
[20] Coefficients of bi-univalent functions with positive real part derivatives http://math.usm.my/bulletin/pdf/acceptedpapers/2013-04-050-R1.pdf (Bull. Malays. Math. Soc., in press)
[21] On a coefficient problem for bi-univalent functions, Proc. Am. Math. Soc., Volume 18 (1967), pp. 63-68
[22] Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal. (2013) (Article ID 573017, 3 p)
[23] 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
[24] On a new subclass of bi-univalent functions, J. Egypt. Math. Soc., Volume 21 (2013) no. 3, pp. 190-193
[25] Coefficient bounds for certain subclasses of analytic functions, J. Math. Anal., Volume 4 (2013) no. 1, pp. 22-27
[26] Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, Volume 27 (2013) no. 5, pp. 831-842
[27] Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., Volume 23 (2010), pp. 1188-1192
[28] Topics in univalent function theory, University of London, 1981 (PhD thesis)
[29] On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., Volume 162 (1991) no. 1, pp. 268-276
[30] Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., Volume 25 (2012), pp. 990-994
[31] A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput., Volume 218 (2012), pp. 11461-11465
Cited by Sources:
Comments - Policy