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.

Some well-known authors have extensively used orthogonal polynomials in the framework of geometric function theory. We are motivated by previous research that has been conducted and, this study, we solve Fekete–Szegö problem as well give bound estimates for coefficients and an upper estimate second Hankel determinant functions class G?(v,?) analytical bi-univalent functions, implicating Euler p...

in this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. upper bounds for the second and third coefficients of functions in this subclass are founded. our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.

The q-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the operator are highlighted explained this research. We then build a novel subclass analytic bi-univalent functions using certain q-Chebyshev polynomials. A number coefficient bounds, as well Fekete–Szegö inequalities second Hankel determinant provided for these newly specified fu...

In the current study, we provide a novel qualitative new subclass of analytical and bi-univalent functions in symmetry domain U defined by use Gegenbauer polynomials. We derive estimates for Fekete–Szegö functional problems Taylor–Maclaurin coefficients a2 a3 that belong to each these subclasses function classes. Some more results are revealed after concentrating on parameters employed our main...

The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class bi-univalent functions defined by means Gegenbauer polynomials with series. For in each these function classes, have derived explored estimates Taylor coefficients a2 a3 Fekete-Szegö functional problems belonging to subclasses.

In this paper we introduce some new subclasses of the class σ of bi-univalent functions and obtain bounds for the initial coefficients of the Taylor series expansion of functions from the considered classes.

In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function σm m-fold symmetric bi-univalent functions defined in open unit disc D and obtain estimates first two Taylor–Maclaurin coefficients for family. Further, Fekete–Szegö functional is also estimated. The results presented paper not only generalize improve some recent works, but give new as cases.