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On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator

Year 2019, Volume: 68 Issue: 1, 776 - 783, 01.02.2019
https://doi.org/10.31801/cfsuasmas.475818

Abstract

The aim of this investigation is to introduce two new subclasses of the class σ related with the generalized Sălăgean differential operator and find estimates on the coefficients |a₂| and |a₃| for functions in these new subclasses. Moreover, we give some interesting results by using the relationship between Sălăgean's differential operator and generalized Sălăgean differential operator.

References

  • Al-Oboudi, F.M., On Univalent Functions Defined by a Generalized Salagean Operator, International Journal of Mathematics and Mathematical Sciences 27(2004), 1429-1436.
  • Ali R.M., Lee S.K., Ravichandran V. and Supramanian S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344-351.
  • Brannan D.A. and Taha T.S., On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Mathematical Analysis and its Applications, Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babe-Bolyai Math., 31(2)(1986), 70-77.
  • Deniz E., Çağlar M. and Orhan H., Second Hankel determinant for bi-starlike and bi-convex functions of oder β, Appl. Math. Comput. 271 (2015), 301-307.
  • Duren P.L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Vol. 259. Springer:New York, NY,USA, 1983.
  • Orhan H., Magesh N. and Balaji V.K., Fekete-Szegö problem for certain classes of Ma-Minda bi-univalent functions, Afr. Math., (2016) 27: 889-897.
  • Orhan H., Toklu E., and Kadıoğlu E., Second Hankel determinant problem for k-bi-starlike functions, Filomat, 31:12 (2017), 3897-3904.
  • Pommerenke C., Univalent Functions. Gottingen, Germany: Vandenhoeck and Rupercht, 1975.
  • Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (10) (2010), 1188-1192.
  • Şeker B., On a new subclass of bi-univalent functions using Salagean operator, Turk J Math, doi: 10.3906/mat-1507-100.(Accepted).
Year 2019, Volume: 68 Issue: 1, 776 - 783, 01.02.2019
https://doi.org/10.31801/cfsuasmas.475818

Abstract

References

  • Al-Oboudi, F.M., On Univalent Functions Defined by a Generalized Salagean Operator, International Journal of Mathematics and Mathematical Sciences 27(2004), 1429-1436.
  • Ali R.M., Lee S.K., Ravichandran V. and Supramanian S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344-351.
  • Brannan D.A. and Taha T.S., On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Mathematical Analysis and its Applications, Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babe-Bolyai Math., 31(2)(1986), 70-77.
  • Deniz E., Çağlar M. and Orhan H., Second Hankel determinant for bi-starlike and bi-convex functions of oder β, Appl. Math. Comput. 271 (2015), 301-307.
  • Duren P.L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Vol. 259. Springer:New York, NY,USA, 1983.
  • Orhan H., Magesh N. and Balaji V.K., Fekete-Szegö problem for certain classes of Ma-Minda bi-univalent functions, Afr. Math., (2016) 27: 889-897.
  • Orhan H., Toklu E., and Kadıoğlu E., Second Hankel determinant problem for k-bi-starlike functions, Filomat, 31:12 (2017), 3897-3904.
  • Pommerenke C., Univalent Functions. Gottingen, Germany: Vandenhoeck and Rupercht, 1975.
  • Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (10) (2010), 1188-1192.
  • Şeker B., On a new subclass of bi-univalent functions using Salagean operator, Turk J Math, doi: 10.3906/mat-1507-100.(Accepted).
There are 10 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Evrim Toklu This is me 0000-0002-2332-0336

İbrahim Aktaş 0000-0003-4570-4485

Fatma Sağsöz 0000-0003-4459-0615

Publication Date February 1, 2019
Submission Date February 19, 2018
Acceptance Date April 12, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Toklu, E., Aktaş, İ., & Sağsöz, F. (2019). On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 776-783. https://doi.org/10.31801/cfsuasmas.475818
AMA Toklu E, Aktaş İ, Sağsöz F. On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):776-783. doi:10.31801/cfsuasmas.475818
Chicago Toklu, Evrim, İbrahim Aktaş, and Fatma Sağsöz. “On New Subclasses of Bi-Univalent Functions Defined by Generalized Sălăgean Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 776-83. https://doi.org/10.31801/cfsuasmas.475818.
EndNote Toklu E, Aktaş İ, Sağsöz F (February 1, 2019) On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 776–783.
IEEE E. Toklu, İ. Aktaş, and F. Sağsöz, “On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 776–783, 2019, doi: 10.31801/cfsuasmas.475818.
ISNAD Toklu, Evrim et al. “On New Subclasses of Bi-Univalent Functions Defined by Generalized Sălăgean Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 776-783. https://doi.org/10.31801/cfsuasmas.475818.
JAMA Toklu E, Aktaş İ, Sağsöz F. On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:776–783.
MLA Toklu, Evrim et al. “On New Subclasses of Bi-Univalent Functions Defined by Generalized Sălăgean Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 776-83, doi:10.31801/cfsuasmas.475818.
Vancouver Toklu E, Aktaş İ, Sağsöz F. On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):776-83.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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