Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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COEFFICIENT ESTIMATES FOR A NEW GENERAL SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS

  • Bulut, Serap (Faculty of Aviation and Space Sciences, Kocaeli University, Arslanbey Campus)
  • Received : 2021.06.21
  • Accepted : 2021.08.11
  • Published : 2021.09.30
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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 |a2| and |a3| for functions belonging to these classes. In this study, we introduce a general subclass 𝔅h,pΣ(λ, μ, 𝛿) of analytic and bi-univalent functions in the unit disk 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.

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References

  1. D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math. 31 (2) (1986), 70-77.
  2. S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43 (2) (2013), 59-65.
  3. S. Bulut, Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions, Filomat 30 (6) (2016), 1567-1575. https://doi.org/10.2298/FIL1606567B
  4. M. Caglar, H. Orhan and N. Yagmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27 (7) (2013), 1165-1171. https://doi.org/10.2298/FIL1307165C
  5. P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.
  6. B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048
  7. H.M. Srivastava, S. Bulut, M. Caglar and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27 (5) (2013), 831-842. https://doi.org/10.2298/FIL1305831S
  8. H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009
  9. 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. https://doi.org/10.1016/j.aml.2011.11.013
  10. 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. https://doi.org/10.1016/j.amc.2012.05.034
  11. 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). https://doi.org/10.1007/s13324-021-00491-7