New Subclasses of Bi-univalent Functions Associated with Quasi-subordination
DOI:
https://doi.org/10.29304/jqcsm.2025.17.22225Keywords:
Analytic functions, Quasi-subordination, Bi-univalent, Majorisation, CoefficientAbstract
In this paper, we obtain some new subclasses of bi-univalent functions by using quasi-subordination. Also, we obtain the bounds for the modulus of the initial coefficients of the function inside these classes.
Downloads
References
O. Altintas and S. Owa, Majorizations and quasi-subordinations for certain analytic functions, Proc. Jpn. Acad. Ser. A, 68(7) (1992), 181-185.
S. Altinkaya, S. Yalcin, Faber Polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I. (2015) (353), 1075-1080.
S. Altinkaya, S.Yalcin, Coefficient bounds for a subclass of bi- univalent functions, TWMS. Journal of Pure and Applied Mathematics, (6) (2015), 180-185.
S. Altinkaya, S.Yalcin, On a new subclass of bi-univalent functions satisfying subordinate conditions, Acta Universitatis Sapientiae, Mathematica (7) (2015), 5-14.
S. R. Bakheet and W.G. Atshan, Third-order sandwich results for analytic univalent functions defined by integral operator. Adv. Mech.2022,10, 1178–1197.
D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes Bolyai Math., 31 (1986), 70-77.
E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Classical Ana. 2 (1), (2013), 49-60.
P. Duren, Subordination, in Complex Analysis, Vol. 599 of Lecture Notes in Mathematics, pp.22-29, Springer, Berlin, Germany, (1977).
P. L. Duren, Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Hidelberg and Tokyo, (1983).
M. El-Ityan, Q. A. Shakir, T. Al-Hawary, R. Buti, D. Breaz, L.-I. Cotîrlă. “On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator,” Mathematics 2025, 13, 1269.
B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011), 1569-1573.
S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close to convex functions, C. R. Acad. Sci. Paris, Ser. I. (2014) (352), 17-20.
S. Kant, Coefficients estimate for certain subclass of bi-univalent functions associated with quasi-subordinations, Journal of fractional calculus and Applied.9 (1) Jan. (2018), 195-203.
M. Lewin, On a coefficient problem for bi-univalent function, Proceedings of the American Mathematical Society, Vol. 18 (1967), 63-68.
W. Ma and D. Minda, Auified treatment of some special classes of univalent functions, Proceedings of the conference on complex analysis, Z. Li. F. Ren, L. Yang and S. Zhang, eds., Int. Press (1994), 157-169.
M. S. Robertson, Quasi-subordination and coefficient conjecture, Bull. Amer. Math. Soc., 76 (1970), 1-9.
M. S . Muhammed and W. G. Atshan, Applications of Quasi-Subordination on Subclasses of bi-univalent Function Associated with Generalized Differential Operator, Journal of Al-Qadisiyah for Computer Science and Mathematics Vol.16(14) 2024.
M. S . Muhammed and W. G. Atshan, Coefficient Estimates and Fekete-Szegö Inequality for a Certain New Subclass of Bi-Univalent Functions by Using Generalized Operator with Bernoulli Polynomials , Advances in Nonlinear Variational Inequalities, 28(4s) (2025),pp.534-546.
M. A. Sabri, W. G. Atshan, E. El-Seidy, New Differential Subordination and Superordination Results for a subclass of Meromorphic Univalent Functions Defined by a New Operator , Iraqi Journal of Science, 2025.
Q. A. Shakir, A. S. Tayyah, D. Breaz, L.-I. Cotîrlă, E. Rapeanu, and F. M. Sakar, “Upper bounds of the third Hankel determinant for bi-univalent functions in crescent-shaped domains,” Symmetry, vol. 16, p. 1281, 2024.
Q. A. Shakir and W. G. Atshan, “On third Hankel determinant for certain subclass of bi-univalent functions,” Symmetry, vol. 16, p. 239, 2024.
A. S. Tayyah, W. G. Atshan, A class of bi-bazilevič and bi-pseudo-starlike functions involving tremblay fractional derivative operator. Probl. Anal. Issues Anal., 14(32)(2)(2025).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Saad Raheem Bakheet, Mohammed Amer Atiyah, Muhammed Salih Muhammed

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.