Coefficient Estimates for Certain General Subclasses of Meromorphic Bi-Univalent Functions

Year 2020, Volume: 8 Issue: 1, 14 - 20, 15.04.2020

Serap Bulut , N. Magesh J. Sivapalan

Abstract

In the present investigation, we introduce two interesting general subclasses of meromorphic and bi-univalent functions. Further, we find estimates on the initial coefficient $|b_{0}|$ and $|b_{1}|$ for functions belonging to these subclasses. Some other closely related results are also represented.

Keywords

univalent functions, bi-univalent functions, meromorphic functions, meromorphic bi-univalent functions, strongly bi-pseudo-starlike functions, bi-pseudo-starlike functions

References

• [1] F. S. Aziz and A. R. S. Juma, Estimating coefficients for subclasses of meromorphic bi-univalent functions associated with linear operator, TWMS J. Appl. Eng. Math. 4 (1) (2014), 39–44.
• [2] S. Bulut, N. Magesh and V. K. Balaji, Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions, C. R. Math. Acad. Sci. Paris 353 (2) (2015), 113–116.
• [3] S. A. Halim, S. G. Hamidi, and V. Ravichandran, Coefficient estimates for meromorphic bi-univalent functions, arXiv:1108.4089, 1–9.
• [4] S. G. Hamidi, S. A. Halim and J. M. Jahangiri, Coefficient estimates for a class of meromorphic bi-univalent functions, C. R. Math. Acad. Sci. Paris 351 (9-10) (2013), 349–352.
• [5] S. G. Hamidi, S. A. Halim and J. M. Jahangiri, Faber polynomial coefficient estimates for meromorphic bi-starlike functions, Int. J. Math. Math. Sci. 2013, Art. ID 498159, 4 pp.
• [6] J. M. Jahangiri and S. G. Hamidi, Coefficients of meromorphic bi-Bazilevic functions, J. Complex Anal. 2014, Art. ID 263917, 4 pp.
• [7] S. Joshi, S. Joshi and H. Pawar, On some subclasses of bi-univalent functions associated with pseudo-starlike functions, J. Egyptian Math. Soc. 24 (4) (2016), 522–525.
• [8] T. Panigrahi, Coefficient bounds for certain subclasses of meromorphic and bi-univalent functions, Bull. Korean Math. Soc. 50 (5) (2013), 1531–1538.
• [9] F. M. Sakar, Estimating coefficients for certain subclasses of meromorphic and bi-univalent functions, J. Inequal. Appl. 2018, 2018:283.
• [10] S. Salehian and A. Zireh, Coefficient estimates for certain subclass of meromorphic and bi-univalent functions, Commun. Korean Math. Soc. 32 (2) (2017), 389–397.
• [11] Y. J. Sim and O. S. Kwon, Certain subclasses of meromorphically bi-univalent functions, Bull. Malays. Math. Sci. Soc. 40 (2) (2017), 841–855.
• [12] H. M. Srivastava, S. B. Joshi, S. S. Joshi and H. Pawar, Coefficient estimates for certain subclasses of meromorphically bi-univalent functions, Palest. J. Math. 5 (Special Issue) (2016), 250–258.
• [13] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (10) (2010), 1188–1192.
• [14] P. P. Vyas and S. Kant, Initial coefficients bounds for an unified class of meromorphic bi-univalent functions, Int. J. Math. Appl., 6(1-B) (2018), 209–114.
• [15] H.-G. Xiao and Q.-H. Xu, Coefficient estimates for three generalized classes of meromorphic and bi-univalent functions, Filomat 29 (7) (2015), 1601–1612.