Coefficient estimates for a subclass of analytic bi-pseudo-starlike functions of Ma-Minda type

Year 2018, Volume: 6 Issue: 2, 306 - 310, 15.10.2018

Serap Bulut

Abstract

In this paper, we introduce a new subclass $\mathcal{LB}_{\Sigma }^{\lambda }\left( \varphi \right) $ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}.$ For functions belonging to this class, we obtain initial coefficient bounds.\ Our results generalize and improve some earlier results in the literature

Keywords

Analytic functions; univalent functions; bi-univalent functions; coefficient bounds; subordination; pseudo-starlike functions.

References

• [1] R.M. Ali, S.K. Lee, V. Ravichandran and S. Supramanian, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344–351.
• [2] D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes¸-Bolyai Math. 31 (2) (1986), 70–77.
• [3] K.O. Babalola, On l-pseudo-starlike functions, J. Class. Anal. 3 (2) (2013), 137–147.
• [4] S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43 (2) (2013), 59–65.
• [5] M. C¸ a˘glar, H. Orhan and N. Ya˘gmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27 (7) (2013), 1165–1171.
• [6] E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2 (1) (2013), 49–60.
• [7] P.L. Duren, Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.
• [8] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569–1573.
• [9] S. Hajiparvaneh and A. Zireh, Coefficient estimates for subclass of analytic and bi-univalent functions defined by differential operator, Tbilisi Math. J. 10 (2) (2017), 91–102.
• [10] S. Joshi, S. Joshi and H. Pawar, On some subclasses of bi-univalent functions associated with pseudo-starlike functions, J. Egyptian Math. Soc. 24 (2016), 522–525.
• [11] E. Mazi and S¸ . Altınkaya, On a new subclass of bi-univalent functions satisfying subordinate conditions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (1) (2019), 724–733.
• [12] H.M. Srivastava, S. Bulut, M. C¸ a˘glar and N. Ya˘gmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27 (5) (2013), 831–842.
• [13] H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192.
• [14] Q.-H. Xu, Y.-C. Gui and H.M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990–994.
• [15] Q.-H. Xu, H.-G. Xiao and H.M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012), 11461–11465.
• [16] P. Zaprawa, Estimates of initial coefficients for bi-univalent functions, Abstr. Appl. Anal. 2014, Art. ID 357480, 1–6.
• [17] A. Zireh and S. Hajiparvaneh, Coefficient bounds for certain subclasses of analytic and bi-univalent functions, Ann. Acad. Rom. Sci. Ser. Math. Appl. 8 (2) (2016), 133–144.
• [18] A. Zireh and S. Hajiparvaneh, Coefficient bounds for certain subclasses of analytic functions, Appl. Math. E-Notes 17 (2017), 177–185.