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.
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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)
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)
Altınkaya, S., Yalçın, S.: Coefficient estimates for a certain subclass of bi-univalent functions. Matematiche (Catania) 71(2), 53–61 (2016)
Brannan, D.A., Taha, T.S.: On some classes of bi-univalent functions. Studia Univ. Babeş-Bolyai Math. 31(2), 70–77 (1986)
Bulut, S.: Coefficient estimates for a class of analytic and bi-univalent functions. Novi Sad J. Math. 43(2), 59–65 (2013)
Çağlar, M., Orhan, H., Yağmur, N.: Coefficient bounds for new subclasses of bi-univalent functions. Filomat 27(7), 1165–1171 (2013)
Deniz, E.: Certain subclasses of bi-univalent functions satisfying subordinate conditions. J. Class. Anal. 2(1), 49–60 (2013)
Duren, P.L.: Univalent functions. In: Grundlehren der Mathematischen Wissenschaften, vol. 259. Springer, New York (1983)
Frasin, B.A., Aouf, M.K.: New subclasses of bi-univalent functions. Appl. Math. Lett. 24, 1569–1573 (2011)
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)
Pommerenke, Ch.: Univalent Functions. Vandenhoeck and Rupercht, G öttingen (1975)
Ronning, F.: A survey on uniformly convex and uniformly starlike functions. Ann. Univ. Mariae Curie-Sklodowska Sect. A 47, 123–134 (1993)
Srivastava, H.M., Mishra, A.K., Gochhayat, P.: Certain subclasses of analytic and bi-univalent functions. Appl. Math. Lett. 23, 1188–1192 (2010)
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)
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)
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)
Zaprawa, P.: Estimates of initial coefficients for bi-univalent functions. Abstr. Appl. Anal. 357480, 1–6 (2014)
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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
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DOI: https://doi.org/10.1007/s13370-018-0543-y
Keywords
- Analytic functions
- Univalent functions
- Bi-univalent functions
- Coefficient bounds
- Subordination
- Parabolic-starlike functions