Korean J. Math.  Vol 29, No 3 (2021)  pp.519-526
DOI: https://doi.org/10.11568/kjm.2021.29.3.519

Coefficient estimates for a new general subclass of analytic bi-univalent functions

Serap Bulut

Abstract


In a very recent paper, Yousef et al. [Anal. Math. Phys. 11: 58 (2021)] introduced two new subclasses of analytic and bi-univalent functions and obtained the estimates on the first two Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ for functions belonging to these classes. In this study, we introduce a general subclass $\mathcal{B}_{\Sigma }^{h,p}\left( \lambda ,\mu ,\delta \right) $ of analytic and bi-univalent functions in the unit disk $\mathbb{U}$, and investigate the coefficient bounds for functions belonging to this general function class. Our results improve the results of the above mentioned paper of Yousef et al.


Keywords


Analytic functions, Univalent functions, Bi-univalent functions, Coefficient bounds

Subject classification

30C45

Sponsor(s)



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References


D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babe ̧s- Bolyai Math. 31 (2) (1986), 70–77. (Google Scholar)

S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43 (2) (2013), 59–65. (Google Scholar)

S. Bulut, Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions, Filomat 30 (6) (2016), 1567–1575. (Google Scholar)

M. C ̧ag ̆lar, H. Orhan and N. Ya ̆gmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27 (7) (2013), 1165–1171. (Google Scholar)

P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983. (Google Scholar)

B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569–1573. (Google Scholar)

H.M. Srivastava, S. Bulut, M. C ̧ a ̆glar and N. Ya ̆gmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27 (5) (2013), 831–842. (Google Scholar)

H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

F. Yousef, S. Alroud and M. Illafe, New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems, Anal. Math. Phys. 11: 58 (2021). (Google Scholar)


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