In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, establish bounds initial coefficients υ2, υ3, and υ4 Taylor–Maclaurin series that Fekete–Szegö functional associated with classes, give many consequences our findings.

In the current work, we introduce a special family of function analytic and m-fold symmetric bi-univalent functions obtain estimates Taylor–Maclaurin coefficients |dm+1| |d2m+1| for in family. For ? real number, Fekete–Szegö functional |d2m+1??dm+12| is also estimated. We indicate several cases defined connections to existing results are discussed.

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization Mittag-Leffler function. The family introduced here is superordinated by conic domain, which impacted Janowski obtain coefficient estimates and subordination conditions for starlikeness Fekete–Szegö functional belonging to class.

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant a certain subclass SL?u,v,? holomorphic functions defined by Carlson-Shaffer operator in unit disk. Finally, some special values parameters, several corollaries were presented.

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z?C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 Fekete–Szegö inequalities a3??a22 these subclasses.