Certain New Subclassess of Analytic and Bi-univalent Functions

Krishna, C. R.; Chandrashekar, A. C.; Ravikumar, N.

doi:10.28924/2291-8639-21-2023-93

Research Article

Certain New Subclassess of Analytic and Bi-univalent Functions

C. R. Krishna
A. C. Chandrashekar
N. Ravikumar*

* Corresponding author

Abstract

The paper presents two novel subclasses of the function class Σ, which consists of bi-univalent functions defined in the open unit disk D={ζ:|ζ|<1}. The authors investigate the properties of these new subclasses and provide estimates for the absolute values of the second, third, and fourth Taylor-Maclaurin coefficients r₂, r₃, and r₄ for functions in these subclasses.

How to Cite

C. R. Krishna, A. C. Chandrashekar, N. Ravikumar, Certain New Subclassess of Analytic and Bi-univalent Functions, Int. J. Anal. Appl. 21 (2023), 93. https://doi.org/10.28924/2291-8639-21-2023-93

BibTeX

@article{Krishna2023,
  author  = {Krishna, C. R. and Chandrashekar, A. C. and Ravikumar, N.},
  title   = {Certain New Subclassess of Analytic and Bi-univalent Functions},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {93},
  doi     = {10.28924/2291-8639-21-2023-93}
}

References

[1] D.A. Brannan, T.S. Taha, On Some Classes of Bi-Univalent Functions, in: Mathematical Analysis and Its Applications, Elsevier, 1988: pp. 53–60. https://doi.org/10.1016/B978-0-08-031636-9.50012-7.
[2] B.A. Frasin, 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.
[3] T. Hayami, S. Owa, Coefficient Bounds for Bi-Univalent Functions, Pan Amer. Math. J. 22 (2012), 15–26.
[4] M. Lewin, On a Coefficient Problem for Bi-Univalent Functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.
[5] X.F. Li, A.P. Wang, Two New Subclasses of Bi-Univalent Functions, Int. Math. Forum, 7 (2012), 1495-1504.
[6] E. Netanyahu, The Minimal Distance of the Image Boundary From the Origin and the Second Coefficient of a Univalent Function in |z| < 1, Arch. Rational Mech. Anal. 32 (1969), 100–112. https://doi.org/10.1007/bf00247676.
[7] C. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, (1975).
[8] N. Ravikumar, S. Latha, On Analytic Functions With Generalized Bounded Variation, Stud. Univ. Babes-Bolyai Math. 57 (2012), 43–52.
[9] H.M. Srivastava, A.K. Mishra, 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.
[10] T.S. Taha, Topics in Univalent Function Theory, Ph.D. Thesis, University of London, (1981).
[11] Q.H. Xu, Y.C. Gui, 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.
[12] Q.H. Xu, H.G. Xiao, 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.