Based on a family of bi-univalent functions introduced through the Faber polynomial expansions and Noor integral operator

<abstract><p>In this study, by using $ q $-analogue of Noor integral operator, we present an analytic and bi-univalent functions family in $ \mathfrak{D} $. We also derive upper coefficient bounds and some important inequalities for the functions in this family by using the Faber polynomial expansions. Furthermore, some relevant corollaries are also presented.</p></abstract>

Certain class of m-fold functions by applying Faber polynomial expansions

"In this paper, we introduce new class $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$ of $m$-fold symmetric bi-univalent functions. Furthermore, we use the Faber polynomial expansions to find upper bounds for the general coefficients $|a_{mk+1}|(k \geqq 2)$ of functions in the class $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$. Moreover, we obtain estimates for the initial coefficients $|a_{m+1}| $ and $|a_{2m+1}|$ for functions in this class. The results presented in this paper would generalize and improve some recent works."

Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

Faber Polynomial for Holomorphic Functions Involving Differential Operator

The purpose of this paper, is to present differential operator for the univalent functions employ a Faber Polynomial . In addition, we will introduce some inclusion properties of the operator that were obtained employ the principle of subordination between holomorphic functions.

Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

Coefficient Bounds for Certain Classes of Analytic Functions Associated with Faber Polynomial

In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By the virtue of the Faber polynomial expansions, the estimation of n−th(n≥3) Taylor–Maclaurin coefficients an is obtained. Furthermore, the bounds value of the first two coefficients of such functions is established.