On the coefficient estimates for a subclass of m-fold symmetric bi-univalent functions
DOI:
https://doi.org/10.24193/subbmath.2025.3.04Keywords:
Analytic functions, Bi-univalent functions, Coefficient estimates, m-fold symmetric bi-univalent functionsAbstract
In this work, we introduce and investigate a subclass \(\mathcal{G}_{\Sigma_m}^{h,p}(\lambda,\gamma)\) of analytic and bi-univalent functions when both \(f\) and \(f^{-1}\) are m-fold symmetric in the open unit disk \(\mathbb{U}\). Moreover, we find upper bounds for the initial coefficients \(|a_{m+1}|\) and \(|a_{2m+1}|\) for functions belonging to this subclass \(\mathcal{G}_{\Sigma_m}^{h,p}(\lambda,\gamma)\). The results presented in this paper would generalize and improve those that were given in several recent works.
References
Altinkaya, S¸., Yal¸cin, S., Coefficient bounds for certain subclasses of mfold symmetric bi-univalent functions, Journal of mathematics, Article ID 241683(2015), 1-5.
Brannan, D. A., Clunie, J. G., (Eds.), Aspects of Contemporary Complex Analysis Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979, (Academic Press, New York and London, 1980).
Brannan, D. A., Taha, T. S., On Some classes of bi-univalent functions, Stud.Univ. Babes-Bolyai Math., 31(1986), no. 2, 70-77.
Duren, P. L., Univalent Functions, Springer-Verlag, New York, Berlin, 1983.
Frasin, B. A., Aouf, M. K., New subclasses of bi-univalent functions, Appl.
Math. Lett. 24(2011), no. 9, 1569-1573.
Hayami, T., Owa, S., Coefficient bounds for bi-univalent functions, PanAmer Math. J. 22(2012), no. 4, 15-26.
Kedzierawski, A. W., Some remarks on bi-univalent functions, Ann. Univ.
Mariae Curie-Sklodowska Sect. A. 39 (1985), 77-81.
Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer.
Math. Soc. 18 (1967) 63-68.
Li , X. F., Wang, A. P., Two new subclasses of bi-univalent functions, International Mathematical Forum. 7(2012),no. 30, 1495-1504.
Motamednezhad, A., Salehian, S., Magesh, N., Coefficient estimates for subclass of m-fold symmetric bi-univalent functions, Kragujevac Journal of Mathematics. 46(2022), no. 3, 395-406.
Srivastava, H. M., Gaboury, S., Ghanim, F., Coefficient estimates for some
subclasses of m-fold symmetric bi-univalent functions, Acta Univ. Apulensis Math. Inform. 41 (2015), 153-164.
Srivastava, H. M., Gaboury, S., Ghanim, F., Initial coefficient estimates for
some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed. 36 (2016), 863-871.
Srivastava, H. M., Sivasubramanian, S., Sivakumar, R., Initial coefficient
bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 7(2014), no. 2, 1-10.
Tan, D. L., Coefficient estimates for bi-univalent functions, Chinese Ann.Math. Ser. A. 5(1984), no. 5, 559-568.
Wanas, A. K., Pall-Szabo, A. O., Coefficient bounds for new subclasses of
analytic and m-fold symmetric bi-univalent functions, Babes-Bolyai Math.
(2021) no. 4, 659-666.
Xu, Q. H., Gui, Y. C., Srivastava, H. M., Coefficient estimates for a certain
subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25(2012), no. 6, 990-994.
Xu, Q. H., Xiao, H. G., Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218(2012), no. 23, 11461-11465.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
