Coefficient Estimates for a Subclass of Bi-univalent Functions (original) (raw)

Coefficient Estimates for a Subclass of Analytic and Bi-Univalent Functions

Bulletin of The Iranian Mathematical Society, 2016

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.

General coefficient estimates for bi-univalent functions; new approach

TURKISH JOURNAL OF MATHEMATICS, 2020

We prove for univalent functions f (z) = z + ∑ ∞ k=n a k z k ; (n ≥ 2) in the unit disk U = {z : |z| < 1}) with f −1 (w) = w + ∑ ∞ k=n b k w k ; (|w| < r0(f), r0(f) ≥ 1 4) that b2n−1 = na 2 n − a2n−1 and b k = −a k for (n ≤ k ≤ 2n − 2). As applications, we find estimates for |an| whenever f is bi-univalent, bi-close-to-convex, bi-starlike, bi-convex, or for bi-univalent functions having positive real part derivatives in U. Moreover, we estimate |na 2 n − a2n−1| whenever f is univalent in U or belongs to certain subclasses of univalent functions. The estimation method can be applied for various subclasses of bi-univalent functions in U and it helps to improve well-known estimates and to generalize some known results as shown in the last section.

Coefficient Estimates for Certain Classes of Bi-Univalent Functions

International Journal of Mathematics and Mathematical Sciences, 2013

A function analytic in the open unit disk D is said to be bi-univalent in D if both the function and its inverse map are univalent there. The bi-univalency condition imposed on the functions analytic in D makes the behavior of their coefficients unpredictable. Not much is known about the behavior of the higher order coefficients of classes of bi-univalent functions. We use Faber polynomial expansions of bi-univalent functions to obtain estimates for their general coefficients subject to certain gap series as well as providing bounds for early coefficients of such functions.

Coefficient estimates for a certain subclass of analytic and bi-univalent functions

Applied Mathematics Letters, 2012

In this paper, we introduce and investigate an interesting subclass H h,p Σ of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class H h,p Σ , we obtain estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |. The results presented in this paper would generalize and improve some recent work of Srivastava et al.

COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF ANALYTIC AND Bi-UNIVALENT FUNCTIONS

2017

In the present paper, we introduce and investigate two new subclasses BΣ(α, λ, μ) andMΣ(β, λ, μ) of bi-valent functions in the unit disk U. For functions belonging to the classes BΣ(α, λ, μ) andMΣ(β, λ, μ), we obtain bounds of the first two Taylor-Maclaurin coefficients of f(z).