Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent Functions Defined by Hadamard Product

Abstract

We introduce and investigate a new general subclass H , Σ ( ; Θ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients | 2 | and | 3 |.

Faber Polynomial Coefficient Estimates for a Comprehensive Subclass of Analytic Bi-Univalent Functions Defined by Subordination

“…In this paper, we use the Faber polynomial expansions to obtain estimates of coefficients |a n | where n ≥ 3, of functions in these subclasses. Consequently, we obtain improvements on the bounds found by Bulut [8] for the first two coefficients |a 2 | and |a 3 | of functions in this subclass.…”

“…Recently, Bulut [8] introduced a comprehensive subclass of analytic bi-univalent functions and obtained non-sharp estimates on the coefficients |a 2 | and |a 3 | for functions in this subclass as follow. Definition 2.1.…”

“…Recently, Bulut [8] introduced a comprehensive subclass H λ,µ Σ (ϕ, Θ) of analytic bi-univalent functions and obtained estimates on the coefficients |a 2 | and |a 3 | for functions in this subclass. In this paper, we use the Faber polynomial expansions to obtain estimates of coefficients |a n | where n ≥ 3, of functions in these subclasses.…”

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

“…From (25) and (26) we obtain the desired estimate of |a 2 | given by (16). Next, from (19) and 21, we have…”

The Second Hankel Determinant Problem for a Class of Bi-Close-to-Convex Functions

“…A function f ∈ A is said to be bi-univalent in D if both f and f −1 are univalent in D, in the sense that f −1 has a univalent analytic continuation to D. Let Σ denote the class of bi-univalent functions in D. For a brief history of functions in the class Σ and also other different characteristics of these functions and the coefficient problems, see [25][26][27][28][29][30][31][32] and the references therein.…”