International Journal of Nonlinear Analysis and Applications

New subclasses of meromorphic bi-univalent functions by associated with ‎subordinate

Document Type : Research Paper

Authors

1 Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran

2 Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran

Abstract

‎In the present paper‎, ‎we define two subclasses Σ(λ‎,‎α‎,‎β)‎, ‎ΣC(α‎,‎β) of meromorphic univalent functions and subclass ΣB,C(α‎,‎β‎,‎λ) of meromorphic bi-univalent functions‎. ‎Furthermore‎, ‎we obtain estimates on the general coefficients |bn| (n≥1) for functions in the subclasses Σ(λ‎,‎α‎,‎β)‎, ‎ΣC(α‎,‎β) and estimates for the early coefficients of functions in subclass ΣB,C(α‎,‎β‎,‎λ) by associated subordination‎. ‎The results obtained in this paper would generalize and improve those in related works of several earlier authors‎.

Keywords

[1] S. G. Hamidi, S. A. Halim, J. M. Jahangiri, Faber polynomial coefficient estimates for meromorphic bi-starlike functions, Int. J. Math. Math. Sci. 2013 (2013), Art. ID 498159, 1–4.
[2] T. Janani and G. Murugusundaramoorthy, Coefficient estimates of meromorphic bi-starlike functions of complex order, Int. J. Anal. Appl. 4 (1) (2014) 68–77.
[3] F. Keogh and E. Merkers, A coefficient inequality for certain classes of analytic functions, Proc. Am. Math. Soc. 20 (1969) 8–12.
[4] K. Kuroki and S. Owa, Notes on new class for certain analytic functions, Adv.Math. Sci. J. 1 (2) (2012) 127–131.
[5] H. Orhan, N. Magesh and V. K. Balaji, Initial coefficient bounds for certain classes of Meromorphic bi-univalent functions, Asian European J. Math. 7(1) (2014) 1–9.
[6] T. Panigrahi, Coefficient bounds for certain subclasses of meromorphic and bi-univalent functions, Bull. Korean Math. Soc. 50(5) (2013) 1531–1538.
[7] C. Pommerenke, Univalent Functions. Vandenhoeck and Ruprecht, G¨ottingen, 1975.
[8] W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc. 48 (1943) 48–82.
[9] S. Salehian and A. Zireh, Coefficient estimate for certain subclass of meromorphic and bi-univalent functions, Commun. Korean Math. Soc. 32(2) (2017) 389–397.
[10] Y. J. Sim and O. S. Kwon, Certain subclasses of meromorphically bi-univalent functions, Bull. Malays. Math. Sci. Soc. 40(2) (2017) 841–855.
[11] H.-G. Xiao, Q.-H. Xu, Coefficient estimates for three generalized classes of meromorphic and bi-univalent functions, Filomat 29(7) (2015) 1601–1612.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 61-74
  • Receive Date: 09 March 2019
  • Accept Date: 14 January 2020