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Coefficient estimates for a subclass of analytic and bi-univalent functions by an integral operator | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 16، دوره 16، شماره 8، آبان 2025، صفحه 179-187 اصل مقاله (389.8 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31429.4627 | ||
| نویسندگان | ||
| Seyed Hadi Hosseini1؛ Ahmad Motamednezhad* 1؛ Safa Salehian2 | ||
| 1Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 316-36155, Shahrood, Iran | ||
| 2Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran | ||
| تاریخ دریافت: 12 تیر 1402، تاریخ بازنگری: 12 مرداد 1402، تاریخ پذیرش: 17 شهریور 1402 | ||
| چکیده | ||
| In this paper, we introduce and investigate a subclass $\mathcal{G}_{\Sigma}^{h,p}(\lambda,m,n, \alpha,\gamma)$ of bi-univalent functions in the open unit disk $\mathbb{U}$. Upper bounds for this class's second and third coefficients of functions are found. The results, which we have presented in this paper, would generalize and improve some recent works of several earlier authors. | ||
| کلیدواژه‌ها | ||
| Analytic functions؛ Bi-univalent functions؛ Coefficient estimates؛ Starlike functions؛ Koebe One-Quarter Theorem | ||
| مراجع | ||
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[1] D.A. Brannan and J.G. Clunie, Aspects of Contemporary Complex Analysis, Academic Press, New York and London, 1980. [2] P.L. Duren, Univalent Functions, Springer-Verlag, New York, Berlin, 1983. [3] B.A. Frasin, Coefficient bounds for certain classes of bi-univalent functions, Hacettepe J. Math. Statist. 43 (2014), no. 3, 383–389. [4] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), no. 9, 1569–1573. [5] C.-Y. Gao and S.-Q. Zhou, Certain subclass of starlike functions, Appl. Math. Comput. 187 (2007), 176–182. [6] T. Hayami and S. Owa, Coefficient bounds for bi-univalent functions, Pan. Amer. Math. J. 22 (2012), no. 4, 15–26. [7] A.W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A. 39 (1985), 77–81. [8] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), no. 1, 63–68. [9] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1, Arch. Rational. Mech. Anal. 32 (1969), 100-112. [10] F.O. Salman and W.G. Atshan, Coefficient estimates for subclasses of bi-univalent functions related by a new integral operator, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 4, 47–54. [11] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23 (2010), 1188–1192. [12] D.L. Tan, Coefficient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A. 5 (1984), 559–568. [13] 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. [14] 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. [15] A. Zireh and E.A. Audegani, Coefficient estimates for a subclass of analytic and bi-univalent functions, Bull. Iran. Math. Soc. 42 (2016), 881–889. | ||
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