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New subclasses of meromorphic bi-univalent functions by associated with subordinate | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 6، دوره 12، شماره 2، بهمن 2021، صفحه 61-74 اصل مقاله (424.69 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.17405.1933 | ||
| نویسندگان | ||
| Safa Salehian* 1؛ Ahmad Motamednezhad2 | ||
| 1Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran | ||
| 2Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran | ||
| تاریخ دریافت: 18 اسفند 1397، تاریخ پذیرش: 24 دی 1398 | ||
| چکیده | ||
| In the present paper, we define two subclasses $\Sigma(\lambda, \alpha, \beta)$, $\Sigma_{\mathcal C}(\alpha, \beta)$ of meromorphic univalent functions and subclass $\Sigma_{{\mathcal B},{\mathcal C}}(\alpha, \beta, \lambda)$ of meromorphic bi-univalent functions. Furthermore, we obtain estimates on the general coefficients $|b_n|~(n \ge1)$ for functions in the subclasses $\Sigma(\lambda, \alpha, \beta)$, $\Sigma_{\mathcal C}(\alpha, \beta)$ and estimates for the early coefficients of functions in subclass $\Sigma_{{\mathcal B},{\mathcal C}}(\alpha, \beta, \lambda)$ by associated subordination. The results obtained in this paper would generalize and improve those in related works of several earlier authors. | ||
| کلیدواژه‌ها | ||
| Meromorphic univalent functions؛ Meromorphic bi-univalent functions؛ Coefficients estimates؛ Subordinate | ||
| مراجع | ||
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[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. | ||
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