COEFFICIENT BOUNDS AND FEKETE-SZEGÖ FUNCTIONAL PROBLEM FOR A NEW SUBCLASS OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

Year 2025, Volume: 15 Issue: 12, 2732 - 2741, 06.12.2025

Ayyub Gorganli Davaji Ahmad Motamednezhad , Safa Salehian

Abstract

This paper introduces a novel subclass of $m$-fold symmetric bi-univalent functions denoted as $\mathcal{S}_{\Sigma_m}^{h.p}$. Precise coefficient estimates for terms $|a_{m+1}| , |a_{2m+1}|$ and the Fekete-Szegö functional are derived for functions belonging to this subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Keywords

Coefficient estimates , $m$-fold symmetric bi-univalent functions , Fekete-Szegö functional problems

Thanks

The authors sincerely thank the referees for their valuable comments and suggestions.

References

• Aldawish, I., Swamy, S. R., Frasin, B. A., (2022), A Special family of m-fold symmetric bi-univalent functions satisfying subordination condition, Fractal Fract., 6(5), pp. 1-13.
• Brannan, D. A., Clunie(Eds.), J. G., (1980), Aspects of contemporary complex analysis, Academic Press, London.
• Brannan, D. A., Taha, T. S., (1986), On Some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math., 31(2), pp. 70-77.
• Dubey, R. S., Shekhawat, N., Vijaywargiya, P., Modi, K., (2023), Certain subclass of m- fold symmetric bi-univalent functions' bounds for initial coefficients, Palest. J. Math., 12(1), pp. 968-975.
• Jadhav, S. D., Patil, A. B., Wani, I. A., (2024), Initial Taylor-Maclurin coefficient bounds and the Fekete-Szeg$\ddot{o}$ problems for subclasses of m-fold symmetric analytic bi-univalent functions, TWMS. J. App. and Eng. Math., 14(1), pp. 185-196.
• Motamednezhad, A., Salehian, S., Magesh, N., (2022), Coefficient estimates for subclass of m-fold Symmetric Bi-univalent Functions, Kragujevac J. Math., 46(3), pp. 395-406.
• Motamednezhad, A., Salehian, S., Magesh, N., (2021), The Fekete-Szegö problems for a subclass of m-fold symmetric bi-univalent functions,TWMS. J. App. and Eng. Math., 11(2), pp. 514-523.
• Koepf, W., (1989), Coefficients of symmetric functions of bounded boundary rotation, Proc. Amer. Math. Soc., 105(2), pp. 324-329.
• Pommerenke, Ch., (1975), Univalent Functions, Vandenhoeck and Ruprecht, Gottingen.
• Salehian, S., Motamednezhad, A., Magesh, N., (2023), Coefficient estimates for a general subclass of m-fold symmetric bi-univalent functions by using Faber polynomials, Iran. J. Math. Sci. Inform., 8(1), pp. 97-108.
• Seker, B., Taymur, I., (2021), On subclasses of m-fold symmetric bi-univalent functions, TWMS. J. App. and Eng. Math., 11(2), pp. 598-604.
• Srivastava, H. M., Gaboury, S., Ghanim, F., (2016), Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B, 36(3), pp. 863-871.
• Srivastava, H. M., Mishra, A. K., Gochhayat, P., (2010), Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(10), pp. 1188-1192.
• Srivastava, H. M., Sumer Eker, S., Rosihan Ali, M., (2015), Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29(8), pp. 1839-1845.
• Srivastava, H. M., Sivasubramanian, S., Sivakumar, R., (2014), Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7(2), pp. 1-10.
• Srivastava, H. M., Zireh, A., Hajiparvaneh, S., (2018), Coefficient estimates for some subclasses of $m$-fold symmetric bi-univalent functions, Filomat, 32(9), pp. 3143-3153.
• Tang, H., Srivastava, H. M., Sivasubramanian, S., Gurusamy, P., (2016), The Fekete-Szegö functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal, 10(4), pp. 1063-1092.
• Tu, Z., Xiong, L., (2018), Coefficient problems for united starlike and convex classes of m-fold symmetric bi-univalent functions, J. Math. Inequal, 12(4), pp. 921-932.
• Wanas, A. K., Raadhi, H. K., (2022), Maclaurin Coefficient Estimates for a New Subclasses of m-fold Symmetric Bi-Univalent Functions, Earthline J. Math. Sci, 11(2), pp. 199-210.
• Zireh, A., Analouei Adegani, E., Bulut, S., (2016), Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin., 23(4), pp. 487-504.