Bounds on Initial Coefficients for a Certain New Subclass of Bi-univalent Functions by Means of Faber Polynomial Expansions

Coefficient Bounds for a New Families of m-Fold Symmetric Bi-Univalent Functions Defined by Bazilevic Convex Functions

“…For a brief history and interesting examples in the family Σ see the pioneering work on this subject by Srivastava et al [25], which actually revived the study of bi-univalent functions in recent years. In a considerably large number of sequels to the aforementioned work of Srivastava et al [25], several different sub families of the bi-univalent function family Σ were introduced and studied analogously by the many authors (see, for example, [1,2,3,5,9,10,11,15,19,23,28,29,30,33]).…”

Coefficient Inequalities and Fekete–Szegö-Type Problems for Family of Bi-Univalent Functions

“…The problem of estimating the coefficient |a n | for n ∈ {4, 5, 6, • • • } remains unresolved (see [2] for more information). Several researchers have investigated different subfamilies of Ω and obtained estimates for the Maclaurin coefficients |a 2 | and |a 3 | (see [3][4][5][6]). Extensive research has been dedicated to the Fekete-Szegö functional, represented as a 3 − κa 2 2 , within the domain of geometric function theory.…”

Two Families of m-fold Symmetric Bi-univalent Functions Involving a Linear Combination of Bazilevic Starlike and Convex Functions

“…For a brief history and interesting examples in the family Σ see the pioneering work on this subject by Srivastava et al [24], which actually revived the study of bi-univalent functions in recent years. In a considerably large number of sequels to the aforementioned work of Srivastava et al [24], several different sub families of the bi-univalent function family Σ were introduced and studied analogously by the many authors (see, for example, [2,3,5,11,15,18,22,27,28,30,33]).…”