Coefficient Bounds for a Family of s-Fold Symmetric Bi-Univalent Functions

Abstract

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications of our main findings using it. A few new and well-known corollaries are studied in order to show the connection between recent and earlier work.

Faber Polynomial Coefficient Inequalities for a Subclass of Bi-Close-To-Convex Functions Associated with Fractional Differential Operator

“…New classes of bi-univalent functions were established by Hamidi and Jahangiri [21,25], who also employed the Faber polynomial expansion approach to establish coefficient bounds. Furthermore, many authors like [26][27][28][29] applied this technique and determined some useful results for bi-univalent functions (see for detail [21,30,31]). We also refer the reader to ( [32][33][34]) for recent papers dealing with bi-close-to-convex functions.…”

Applications of Horadam Polynomials for Bazilevič and λ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions

“…Furthermore, many authors have introduced and studied numerous subclasses of the bi-univalent function family Σ, analogously to the work by Srivastava et al [5]. However, several recent papers have only provided non-sharp estimates on the initial coefficients |a 2 | and |a 3 | in the Taylor Maclaurin expansion (1) (see, for example, [6][7][8][9][10][11][12][13]). The general coefficient bounds |a n | for n ∈ N with n ≧ 3 for functions f ∈ Σ have not been fully addressed for many subfamilies of Σ (see for example [14]).…”

“…where Φ(δ, η, λ, t), Ψ(δ, η, λ, t) and ∆(δ, η, λ, t) are given by ( 5), ( 6) and (7), respectively. Using (3), ( 14) and ( 22), by further computations, we have…”

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

“…Furthermore, many authors (see, for example, Refs. [42][43][44][45][46][47][48][49][50][51]) applied the technique of Faber polynomials and determined some interesting results for bi-univalent functions (see, for details, Ref. [44]).…”