Skip to main content
Log in

Coefficient estimates for a subclass of parabolic bi-starlike functions

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disk \(\mathbb {U}\). For functions belonging to this class, we obtain initial coefficient bounds and Fekete–Szegö inequality.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ali, R.M., Singh, V.: Coefficients of parabolic starlike functions of order $\rho $, Computational Methods and Function Theory 1994 (Penang), Ser. Approx. Decompos., vol. 5, pp. 23–36. World Scientific Publishing, New Jersey (1995)

  2. Altınkaya, S., Yalçın, S.: Coefficient estimates for two new subclasses of biunivalent functions with respect to symmetric points. J. Funct. Spaces, Art. ID 145242 (2015)

  3. Altınkaya, S., Yalçın, S.: Coefficient estimates for a certain subclass of bi-univalent functions. Matematiche (Catania) 71(2), 53–61 (2016)

    MathSciNet  MATH  Google Scholar 

  4. Brannan, D.A., Taha, T.S.: On some classes of bi-univalent functions. Studia Univ. Babeş-Bolyai Math. 31(2), 70–77 (1986)

    MathSciNet  MATH  Google Scholar 

  5. Bulut, S.: Coefficient estimates for a class of analytic and bi-univalent functions. Novi Sad J. Math. 43(2), 59–65 (2013)

    MathSciNet  MATH  Google Scholar 

  6. Çağlar, M., Orhan, H., Yağmur, N.: Coefficient bounds for new subclasses of bi-univalent functions. Filomat 27(7), 1165–1171 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Deniz, E.: Certain subclasses of bi-univalent functions satisfying subordinate conditions. J. Class. Anal. 2(1), 49–60 (2013)

    Article  MathSciNet  Google Scholar 

  8. Duren, P.L.: Univalent functions. In: Grundlehren der Mathematischen Wissenschaften, vol. 259. Springer, New York (1983)

  9. Frasin, B.A., Aouf, M.K.: New subclasses of bi-univalent functions. Appl. Math. Lett. 24, 1569–1573 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ma, W.C., Minda, D.: A unified treatment of some special classes of univalent functions. In: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Conf. Proc. Lecture Notes Anal., I, pp. 157–169. International Press, Massachusetts (1994)

  11. Pommerenke, Ch.: Univalent Functions. Vandenhoeck and Rupercht, G öttingen (1975)

    MATH  Google Scholar 

  12. Ronning, F.: A survey on uniformly convex and uniformly starlike functions. Ann. Univ. Mariae Curie-Sklodowska Sect. A 47, 123–134 (1993)

    MathSciNet  MATH  Google Scholar 

  13. Srivastava, H.M., Mishra, A.K., Gochhayat, P.: Certain subclasses of analytic and bi-univalent functions. Appl. Math. Lett. 23, 1188–1192 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu, Q.-H., Gui, Y.-C., Srivastava, H.M.: Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Appl. Math. Lett. 25, 990–994 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu, Q.-H., Xiao, H.-G., Srivastava, H.M.: A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems. Appl. Math. Comput. 218, 11461–11465 (2012)

    MathSciNet  MATH  Google Scholar 

  17. Zaprawa, P.: Estimates of initial coefficients for bi-univalent functions. Abstr. Appl. Anal. 357480, 1–6 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Serap Bulut.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bulut, S. Coefficient estimates for a subclass of parabolic bi-starlike functions. Afr. Mat. 29, 331–338 (2018). https://doi.org/10.1007/s13370-018-0543-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-018-0543-y

Keywords

Mathematics Subject Classification

Navigation