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.
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.
Keywords
Analytic bi-concave functions analytic function univalent function bi-univalent function concave function
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Review Articles |
| Authors | |
| 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
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
