Cofficient estimates for a general Subclass of bi-univalent functions
DOI:
https://doi.org/10.5269/bspm.51659Abstract
‎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.
References
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10. 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
11. Xiao-Fei-li, An-Ping Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum. 7, 1495-1504, (2012).
12. 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
13. 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
2. 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.
3. 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
4. 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
5. Duren, P. L., Univalent Functions, Springer-Verlag, New York, Berlin, 1983.
6. 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
7. 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
8. 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
9. 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
10. 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
11. Xiao-Fei-li, An-Ping Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum. 7, 1495-1504, (2012).
12. 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
13. 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
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2022-02-04
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