Cofficient estimates for a general Subclass of bi-univalent functions
Résumé
In this paper, we introduce and investigate an interesting subclass ${\cal{S}}^{h,p}_{\Sigma}(A,B,C,\lambda)$ of bi-univalent functions in the open unit disk $\mathbb{U}$. Furthermore, we find estimates on the $|a_2|$ and $|a_3|$ coefficients for functions in this subclass. The coefficient bounds presented here generalize some recent works of several earlier authors.
Téléchargements
Références
Brannan, D. A., Taha, T. S., On some classes of bi-univalent functions, Studia Universitatis Babes-Bolyai, Series Mathematica 31, 70-77, (1986).
Brannan, D. A., Clunie, J., Aspect of contemporary complex analysis, Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham, Academic Press, New york and London, 1980.
Breaz, D., Breaz, N., Sirvastava, H. M., An extention of the univalent conditions for a family of integral operators, Appl. Math. Lett. 22, 41-44, (2009). https://doi.org/10.1016/j.aml.2007.11.008
Caglar, M., Orhan, H., Ya˘gmur, N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat. 27, 1165-1171, (2013). https://doi.org/10.2298/FIL1307165C
Duren, P. L., Univalent Functions, Springer-Verlag, New York, Berlin, 1983.
Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18, 63-68, (1967). https://doi.org/10.1090/S0002-9939-1967-0206255-1
Magesh, N., Yamini, J., Coefficient bounds for a certain subclass of bi-univalent functions , International Mathematical Forum. 8, 1337-1344, (2013). https://doi.org/10.12988/imf.2013.3595
Netanyahu, E., The minimal distance of the image boundryfromthe origin and second coefficient of a univalent functions in |z| < 1, Arch. Rational Mech. Anal. 32, 100-112, (1969). https://doi.org/10.1007/BF00247676
Srivastava, H. M., Bulut, S., Caglar, M., Ya˘gmur,r, N., Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat. 27, 831-842, (2013). https://doi.org/10.2298/FIL1305831S
Srivastava, H. M., Mishra, A. K., Gochhayat, P., Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23, 1188-1192, (2010). https://doi.org/10.1016/j.aml.2010.05.009
Xiao-Fei-li, An-Ping Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum. 7, 1495-1504, (2012).
Zireh, A., Analouei Adegani, E., Bulut, S., Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin., 23, 487-504, (2016). https://doi.org/10.36045/bbms/1480993582
Zireh, A., Analouei Adegani, E., Bidkham, M., Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate, Math. Slovaca, 68, 369-378, (2018). https://doi.org/10.1515/ms-2017-0108
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
