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COEFFICIENT BOUNDS FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH DZIOK-SRIVASTAVA OPERATOR

  • Received : 2021.11.17
  • Accepted : 2022.01.24
  • Published : 2022.03.30

Abstract

In this article, we represent and examine a new subclass of holomorphic and bi-univalent functions defined in the open unit disk 𝖀, which is associated with the Dziok-Srivastava operator. Additionally, we get upper bound estimates on the Taylor-Maclaurin coefficients |a2| and |a3| of functions in the new class and improve some recent studies.

Keywords

Acknowledgement

A part of this research was carried out while the second author was visiting the University of Alberta. The authors are grateful to professor Sibel Yal,cin for her comments.

References

  1. R. M. Ali, S. K. Lee, V. Ravichandran and S. Subramaniam, Coefficient estimates for biunivalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (2012), 344-351. https://doi.org/10.1016/j.aml.2011.09.012
  2. M. K. Aouf, R. M. El-Ashwah, and A. Abd-Eltawab, New Subclasses of Biunivalent Functions Involving Dziok-Srivastava Operator, ISRN Mathematical Analysis (2013), Article ID 387178, 5 pages.
  3. D. A. Brannan and J. G. Clunie (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).
  4. P. L. Duren, Univalent Functions, Springer-Verlag, New York, Berlin, 1983.
  5. J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13. https://doi.org/10.1016/S0096-3003(98)10042-5
  6. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7-18. https://doi.org/10.1080/10652460304543
  7. T. Hayami and S. Owa, Coefficient bounds for bi-univalent functions, PanAm. Math. J. 22 (2012), 15-26.
  8. 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
  9. A. W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ. Mariae Curie Sklodowska Sect. A. 39 (1985), 77-81.
  10. M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68. https://doi.org/10.1090/S0002-9939-1967-0206255-1
  11. M.M. Shabani and S. Hashemi Sababe, On Some Classes of Spiral-like Functions Defined by the Salagean Operator, Korean J. Math. 28 (2020), 137-147. https://doi.org/10.11568/kjm.2020.28.1.137
  12. M.M. Shabani, Maryam Yazdi and S. Hashemi Sababe, Coefficient Bounds for a Subclass of Harmonic Mappings Convex in one direction, KYUNGPOOK Math. J. 61 (2021), 269-278 https://doi.org/10.5666/KMJ.2021.61.2.269
  13. M.M. Shabani, Maryam Yazdi and S. Hashemi Sababe, Some distortion theorems for new subclass of harmonic univalent functions, Honam Mathematical J. 42(4) (2020), 701-717. https://doi.org/10.5831/HMJ.2020.42.4.701
  14. H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23 (2010), 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009
  15. D. L. Tan, Coefficient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A. 5 (1984), 559-568.
  16. 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
  17. Q. H. Xu, H.G. Xiao, and H. M. Srivastava, A certain general subclass of analytic and biunivalent functions and associated cofficient estimate problems, Appl. Math. Comput. 218 (2012), 11461-11465. https://doi.org/10.1016/j.amc.2012.05.034