Quasi subordinations for bi-univalent functions with symmetric conjugate points

Abstract

Many researchers have recently acquainted and researched several interesting subfamilies of bi-univalent function family 𝛿 and they have found non-sharp estimates on the first two Tay-lor-Maclaurin coefficients |𝑎2| and |𝑎3|. In this current work, the subfamily of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients |𝑎2|, |𝑎3| and besides related with these coefficients |𝑎3 − 𝑎22| for functions belonging to this subfamily are derived. Further some corollaries are also presented.

Keywords

• Bi-Univalent Functions
• Quasi- Subordinations
• Symmetric Conjugate Points

References

1. REFERENCES
2. [1] Akgül A. On second-order differential subordinations for a class of analytic functions defined by convolution. J Nonlinear Sci Appl 2017;10:954963. [CrossRef]
3. [2] Altınkaya Ş, Yalçın S. Coefficient estimates for a certain subclass of bi-univalent functions. J. Le Mathematiche 2016;71:5361.
4. [3] Altıntaş O, Owa S. Majorizations and quasi-subordinations for certain analytic functions. Proc Japan Acad Ser A Math Sci 1992;68:181185.
5. [4] Brannan DA, Taha TS. On some classes of bi-univalent functions. Stud Univ Babe-Bolyai Math 1986;31:7077.
6. [5] Duren PL. Univalent Functions. New York , Ny, USA: Springer-Verlag; 1983.
7. [6] El-Ashwah R, Kanas S. Fekete-Szegö inequalities for quasi-subordination functions classes of complex order. Kyungpook Math J 2015;55:679688. [CrossRef]
8. [7] El-Ashwah RM, Thomas DK. Some subclasses of close-to-convex functions. J Ramanujan Math Soc 1987;2:85100.

9. [8] Hamidi SG, Jahangiri JM. Faber polynomial coefficient estimates for analytic bi close-to-convex functions. Compt Rendus Acad Sci Math 2014;352:1720. [CrossRef]
10. [9] Ma W, Minda D. A unified treatment of some special classes of univalent functions. In Proceedings of the Conference on Complex Analysis, Tianjin, 1992; Conference Proceedings and Lecture Notes in Analysis I; International Press: Cambridge, Massachusets, 1994. p. 157169.
11. [10] Macgregor TH. Majorization by univalent functions. Duke Math. J 1967;34:95102. [CrossRef]
12. [11] Ren F, Owa S, Fukui S. Some inequalities on quasi-subordinate functions. Bull Austral Math Soc 1991;43:317324. [CrossRef]
13. [12] Robertson MS. Quasi-subordination and coefficientsconjectures. Bull Am Math Soc 1970;76:19. [CrossRef]
14. [13] Sivasubramanian S, Sivakumar R, Kanas S, Kim S-A. Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions. Ann Pol Math 2015;113:295304. [CrossRef]
15. [14] Srivastava HM, Mishra AK, Gochhayat P. Certain subclasses of analytic and bi-univalent function. Appl Math Lett 2010;23:11881192. [CrossRef]
16. [15] Srivastava HM, Sümer Eker S, Ali RM. Coefficient bounds for a certain class of analytic and bi-univalent functions. Filomat 2015;29:18391845. [CrossRef]
17. [16] Wanas AK, Majeed AH. Chebyshev polynomial bounded for analytic and bi-univalent functions with respect to symmetric conjugate points. Appl Math E-Notes 2019;19:1421.
18. [17] Xu QH, Gu YC, Srivastava HM. Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Appl Math Lett 2012;25:990994. [CrossRef]