In this paper, two new subclasses of holomorphic and bi-univalent functions are introduced by using Balancing polynomials. Then, coefficient estmations determined for the first coefficients belonging to these classses. Finally, Fekete-Szeg¨o problem is handled in defined.

In this paper, we introduce and investigate new subclasses (Yamakawa-type bi-starlike functions another class of Lashin, both mentioned in the reference list) bi-univalent defined open unit disk, which are associated with Gegenbauer polynomials satisfy subordination conditions. Furthermore, find estimates for Taylor–Maclaurin coefficients |a2| |a3| these subclasses. Several known or consequence...

For a certain subclass of Bazilevic functions, Faber polynomials expansions are used to obtain bi-univalent properties. Estimates on the $n$th Taylor-Maclaurin coefficients functions in this class found. Moreover, some special cases also indicated.

The main purpose of this paper is to obtain an upper bound for the second Hankel determinant functions belonging a subclass bi-univalent in open unit disk complex plane. Furthermore, presented results work improve or generalize recent works other authors.

In this article, we establish the bounds for initial Taylor–Maclaurin coefficients |a2| and |a3| a new family G?(?,?,?;h) of holormorphic bi-univalent functions which involve prestarlike functions. Furthermore, investigate Fekete–Szegö type inequality, special cases consequences.

In this paper, we define certain families SE*(?) and CE(?) of holomorphic bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö type inequalities these families.

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 this work, we introduce a new subclas of bi-univalent functions which is defined by Hadamard product andsubordination in the open unit disk. and find upper bounds for second third coefficients subclass. Further, generalize improve some previously published results.

The motivation of the present article is to define (p−q)-Wanas operator in geometric function theory by symmetric nature quantum calculus. We also initiate and explore certain new families holormorphic bi-univalent functions AE(λ,σ,δ,s,t,p,q;ϑ) SE(μ,γ,σ,δ,s,t,p,q;ϑ) which are defined unit disk U associated with operator. upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö-type i...