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Year 2019, Volume: 68 Issue: 1, 53 - 60, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443600

Abstract

References

  • Altınkaya, Ş. and Yalçın, S., General Properties of Multivalent Concave Functions Involving Linear Operator of Carlson-Shaffer Type, Comptes rendus de l'Academie bulgare des Sciences, 69 12(2016), 1533-1540.
  • Avkhadiev, F. G., Pommerenke, C. and Wirths, K.-J., Sharp inequalities for the coefficient of concave schlicht functions, Comment. Math. Helv. 81(2006), 801-807.
  • Avkhadiev F. G. and Wirths, K.-J., Concave schlicht functions with bounded opening angle at infinity, Lobachevskii J. Math. 17(2005), 3-10.
  • Bayram, H. and Altınkaya, Ş., General Properties of Concave Functions Defined by the Generalized Srivastava-Attiya Operator, Journal of Computational Analysis and Applications, 23 3(2017), 408-416.
  • Bulut, S., Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43(2013), no. 2, 59-65.
  • Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions , Studia Univ. Babes-Bolyai Math. 2(1986), no. 31, 70-77.
  • Cruz, L. and Pommerenke, C., On concave univalent functions , Complex Var. Elliptic Equ. 52(2007), 153-159.
  • Duren, P. L., Univalent functions , In. Grundlehren der Mathematischen Wissenschaften, vol. 259, New York: Springer1983.
  • Frasin, B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24(2011), 1569-1573.
  • Lewin, M., On a coefficient problem for be univalent functions , Proc Amer Math. Soc, 18(1967), 63-68.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions , Appl. Math. Lett. 23(2010), 1188-1192.
  • Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 23(2012), no. 218, 11461-11465.
  • Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25(2012), 990-994.

Coefficient estimates for bi-concave functions

Year 2019, Volume: 68 Issue: 1, 53 - 60, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443600

Abstract

In this study,a new class C_{Σ}^{p,q}(α) of analytic and bi-concave functions were presented in the open unit disc. The coefficients estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| were found for functions belonging to this class.

References

  • Altınkaya, Ş. and Yalçın, S., General Properties of Multivalent Concave Functions Involving Linear Operator of Carlson-Shaffer Type, Comptes rendus de l'Academie bulgare des Sciences, 69 12(2016), 1533-1540.
  • Avkhadiev, F. G., Pommerenke, C. and Wirths, K.-J., Sharp inequalities for the coefficient of concave schlicht functions, Comment. Math. Helv. 81(2006), 801-807.
  • Avkhadiev F. G. and Wirths, K.-J., Concave schlicht functions with bounded opening angle at infinity, Lobachevskii J. Math. 17(2005), 3-10.
  • Bayram, H. and Altınkaya, Ş., General Properties of Concave Functions Defined by the Generalized Srivastava-Attiya Operator, Journal of Computational Analysis and Applications, 23 3(2017), 408-416.
  • Bulut, S., Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43(2013), no. 2, 59-65.
  • Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions , Studia Univ. Babes-Bolyai Math. 2(1986), no. 31, 70-77.
  • Cruz, L. and Pommerenke, C., On concave univalent functions , Complex Var. Elliptic Equ. 52(2007), 153-159.
  • Duren, P. L., Univalent functions , In. Grundlehren der Mathematischen Wissenschaften, vol. 259, New York: Springer1983.
  • Frasin, B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24(2011), 1569-1573.
  • Lewin, M., On a coefficient problem for be univalent functions , Proc Amer Math. Soc, 18(1967), 63-68.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions , Appl. Math. Lett. 23(2010), 1188-1192.
  • Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 23(2012), no. 218, 11461-11465.
  • Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25(2012), 990-994.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

F. Müge Sakar 0000-0002-3884-3957

H. Özlem Güney 0000-0002-3010-7795

Publication Date February 1, 2019
Submission Date February 10, 2017
Acceptance Date October 13, 2017
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Sakar, F. M., & Güney, H. Ö. (2019). Coefficient estimates for bi-concave functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 53-60. https://doi.org/10.31801/cfsuasmas.443600
AMA Sakar FM, Güney HÖ. Coefficient estimates for bi-concave functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):53-60. doi:10.31801/cfsuasmas.443600
Chicago Sakar, F. Müge, and H. Özlem Güney. “Coefficient Estimates for Bi-Concave Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 53-60. https://doi.org/10.31801/cfsuasmas.443600.
EndNote Sakar FM, Güney HÖ (February 1, 2019) Coefficient estimates for bi-concave functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 53–60.
IEEE F. M. Sakar and H. Ö. Güney, “Coefficient estimates for bi-concave functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 53–60, 2019, doi: 10.31801/cfsuasmas.443600.
ISNAD Sakar, F. Müge - Güney, H. Özlem. “Coefficient Estimates for Bi-Concave Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 53-60. https://doi.org/10.31801/cfsuasmas.443600.
JAMA Sakar FM, Güney HÖ. Coefficient estimates for bi-concave functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:53–60.
MLA Sakar, F. Müge and H. Özlem Güney. “Coefficient Estimates for Bi-Concave Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 53-60, doi:10.31801/cfsuasmas.443600.
Vancouver Sakar FM, Güney HÖ. Coefficient estimates for bi-concave functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):53-60.

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

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