Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF GENERAL SUBCLASSES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER INVOLVING SUBORDINATION

  • Altinkaya, Sahsene (Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University) ;
  • Yalcin, Sibel (Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University)
  • Received : 2017.10.27
  • Accepted : 2018.07.31
  • Published : 2018.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

The object of this paper to construct a new class $$A^m_{{\mu},{\lambda},{\delta}}({\alpha},{\beta},{\gamma},t,{\Psi})$$ of bi-univalent functions of complex order defined in the open unit disc. The second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass are determined. Several special consequences of the results are also indicated.

Keywords

References

  1. F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 27 (2004), 1429-1436.
  2. A. Akgul, S. Bulut, On a certain subclass of meromorphic functions defined by Hilbert Space operator, Acta Universitatis Apulensis 45 (2016), 1-9.
  3. A. Akgul, A new subclass of meromorphic functions defined by Hilbert Space operator, Honam Mathematical J. 38 (2016), 495-506. https://doi.org/10.5831/HMJ.2016.38.3.495
  4. S. Altinkaya, S. Yalcin, Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C.R. Acad. Sci. Paris, Ser. I 353 (2015), 1075-1080. https://doi.org/10.1016/j.crma.2015.09.003
  5. S. Altinkaya, S. Yalcin, Coefficient problem for certain subclasses of bi-univalent functions defined by convolution, Math. Morav. 20 (2016), 15-21. https://doi.org/10.5937/MatMor1602015A
  6. D. A. Brannan, J. G. Clunie, Aspects of contemporary complex analysis, New York: Proceedings of the NATO Advanced Study Institute Held at University of Durham, 1979.
  7. D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babes-Bolyai Mathematica 31 (1986), 70-77.
  8. R. Bucur, L. Andrei, D. Breaz, Coefficient bounds and Fekete-Szego problem for a class of analytic functions defined by using a new differential operator, Applied Mathematical Sciences 9 (2015), 1355-1368. https://doi.org/10.12988/ams.2015.511
  9. M. Darus, R. W. Ibrahim, New classes containing generalization of differential operator, Appl. Math. Sci. 3 (2009), 2507-2515.
  10. A. Amourah, Maslina Darus, Some properties of a new class of univalent functions involving a new generalized differential operator with negative coefficients, Indian Journal of Science and Technology 9 (2016), 1-7.
  11. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Bd. 259, Springer-Verlag, Berlin, Heidelberg, New York and Tokyo, 1983.
  12. S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris, Ser. I 354 (2016), 365-370. https://doi.org/10.1016/j.crma.2016.01.013
  13. T. Hayami, S. Owa, Coefficient bounds for bi-univalent functions, Pan Amer. Math. 22 (2012), 15-26.
  14. S. Kanas, H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform. Spec. Funct. 9 (2000), 121-132. https://doi.org/10.1080/10652460008819249
  15. 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
  16. N. Magesh, T. Rosy, S. Varma, Coefficient estimate problem for a new subclass of bi-univalent functions, J. Complex Anal. Art. ID 474231, (2013), 1-3.
  17. T. Panigarhi, G. Murugusundaramoorthy, Coefficient bounds for Bi-univalent functions analytic functions associated with Hohlov operator, Proc. Jangjeon Math. Soc. 16 (2013), 91-100.
  18. E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $\left|z\right|$ < 1, Archive for Rational Mechanics and Analysis 32 (1969), 100-112. https://doi.org/10.1007/BF00247676
  19. Z. Peng, G. Murugusundaramoorthy, T. Janani, Coefficient estimate of biunivalent functions of complex order associated with the Hohlov operator, Journal of Complex Analysis 2014 (2014), Article ID 693908, 1-6.
  20. Ch. Pommerenke, Univalent functions, Vandenhoeck and Rupercht, Gttingen, 1975.
  21. F. Muge Sakar, H. Ozlem Guney, Faber polynomial coefficient bounds for analytic bi-close-to-convex functions defined by fractional calculus, Journal of Fractional Calculus and Applications 9 (2018), 64-71.
  22. G. S. Salagean, Subclasses of Univalent Functions, Complex Analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983.
  23. H. M. Srivastava, G. Murugusundaramoorthy, N. Magesh, Certain subclasses of bi-univalent functions associated with the Hohlov operator, Appl. Math. Lett. 1 (2013), 67-73.
  24. 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
  25. S. R. Swamy, Inclusion properties of certain subclasses of analytic functions, International Mathematical Forum 7 (2012), 1751-1760.