[1] Aldweby, H., Darus, M.: 
On a subclass of bi-univalent functions associated with $q$-derivative operator. J. Math. Computer Sci. 19 (2019), 58–64. 
DOI 10.22436/jmcs.019.01.08[2] Amourah, A., Frasin, B.A., Al-Hawary, T.: 
Coefficient estimates for a subclass of bi-univalent functions associated with symmetric $q$-derivative operator by means of the Gegenbauer polynomials. Kyungpook Math. J. 62 (2) (2022), 257–269. 
MR 4448623[3] Amourah, A., Frasin, B.A., Seoudy, T.M.: 
An application of Miller-Ross type Poisson distribution on certain subclasses of bi-univalent functions subordinate to Gegenbauer polynomials. Mathematics 10 (2022), 10 pp., 2462. 
DOI 10.3390/math10142462 | 
MR 4345706[5] Brannan, D.A., Taha, T.S.: 
On some classes of bi-univalent functions. Mathematical Analysis and its Applications (Mazhar, S.M., Hamoni, A., Faour, N.S., eds.), KFAS Proceedings Series, vol. 3, Kuwait; February 18-21, 1985, Pergamon Press, Elsevier Science Limited, Oxford, 1988, See also Studia Univ. Babes-Bolyai Math., 1986, 31(2): 70-77, pp. 53–60. 
MR 0951657[6] Bulut, S.: 
Certain subclasses of analytic and bi-univalent functions involving the $q$-derivative operator. Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 66 (1) (2017), 108–114. 
DOI 10.1501/Commua1_0000000780 | 
MR 3611862[7] Duren, P.L.: 
Univalent Functions. Grundlehren der Mathematishen Wissenschaften, Springer, New York, 1983. 
MR 0708494 | 
Zbl 0514.30001[8] Frasin, B.A.: 
Subordination results for a class of analytic functions defined by a linear operator. J. Inequ. Pure Appl. Math. 7 (4) (2006), 7 pp., Article 134. 
MR 2268588[10] Jackson, F.H.: 
On $q$-functions and a certain difference operator. Trans. Royal Soc. Edinburgh 46 (1908), 253–281. 
DOI 10.1017/S0080456800002751[11] Jackson, F.H.: On $q$-definite integrals. Quarterly J. Pure Appl. Math. 41 (1910), 193–203.
[14] Li, X.F., Wang, A.P.: 
Two new subclasses of bi-univalent functions. Int. Math. Forum 7 (30) (2012), 1495–1504. 
MR 2967369[15] Madian, S.M.: 
Some properties for certain class of bi-univalent functions defined by $q$-Catas operator with bounded boundary rotation. AIMS Math. 7 (1) (2021), 903–914. 
DOI 10.3934/math.2022053 | 
MR 4332416[17] Mocanu, P.T.: 
Une propriete de convexite géenéralisée dans la théorie de la représentation conforme. Mathematica (CLUJ) 11 (34) (1969), 127–133. 
MR 0273000[18] Páll-Szabó, A.O., Oros, G.I.: 
Coefficient related studies for new classes of bi-univalent functions. Mathematics 8 (2020), 1110. 
DOI 10.3390/math8071110[19] Polatoglu, Y., Bolkal, M., Sen, A., Yavuz, E.: 
A study on the generalization of Janowski function in the unit disc. Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. 22 (2006), 27–31. 
MR 2216764[20] Rahmatan, H., Shokri, A., Ahmad, H., Botmart, T.: 
Subordination method for the estimation of certain subclass of analytic functions defined by the $q$-derivative operator. J. Funct. Spaces, 9 pages, Article Id. 5078060. 
MR 4429892[21] Seoudy, T.M., Aouf, M.K.: 
Coefficient estimates of new classes of $q$-starlike and $q$-convex functions of complex order. J. Math. Inequal. 10 (2016), 135–145. 
DOI 10.7153/jmi-10-11 | 
MR 3455309[22] Singh, Gagandeep: Coefficient estimates for bi-univalent functions with respect to symmetric points. J. Nonlinear Funct. Anal. 1 (2013), 1–9.
[23] Singh, Gurmeet, Singh, Gagandeep, Singh, Gurcharanjit: 
Certain subclasses of Sakaguchi-type bi-univalent functions. Ganita 69 (2) (2019), 45–55. 
MR 4060858[24] Singh, Gurmeet, Singh, Gagandeep, Singh, Gurcharanjit: 
A generalized subclass of alpha-convex bi-univalent functions of complex order. Jnanabha 50 (1) (2020), 65–71. 
DOI 10.58250/jnanabha.2020.50108 | 
MR 3962610[25] Singh, Gurmeet, Singh, Gagandeep, Singh, Gurcharanjit: 
Certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. General Mathematics 28 (1) (2020), 125–140. 
DOI 10.2478/gm-2020-0010 | 
MR 3962610[26] Sivapalan, J., Magesh, N., Murthy, S.: 
Coefficient estimates for bi-univalent functions with respect to symmetric conjugate points associated with Horadam Polynomials. Malaya J. Mat. 8 (2) (2020), 565–569. 
DOI 10.26637/MJM0802/0042 | 
MR 4112566[28] Srivastava, H.M., Sümer, S.: 
Some applications of a subordination theorem for a class of analytic functions. Appl. Math. Lett. 21 (4) (2008), 394–399. 
DOI 10.1016/j.aml.2007.02.032 | 
MR 2406520[29] Toklu, E.: A new subclass of bi-univalent functions defined by $q$-derivative. TWMS J. App. Engg. Math. 9 (2019), 84–90.
[30] Venkatesan, M., Kaliappan, V.: New subclasses of bi-univalent functions associated with $q$-calculus operator. Int. J. Nonlinear Anal. Appl. 13 (2) (2022), 2141–2149.