Abstract
In a very recent work, Seker [Seker B. On a new subclass of bi-univalent functions defined by using Salagean operator. Turkish Journal of Mathematics 2018; 42: 2891-2896] defined two subclasses of analytic bi-univalent functions by means of Salagean differential operator and he obtained the initial Taylor-Maclaurin coefficient estimates for functions belonging to these classes. The main purpose of this paper is to improve the results obtained by Seker in the aforementioned study. For this purpose, we define a general subclass of bi-univalent functions.
Highlights
Let A be the family of analytic functions
We introduce the a new subclass of A which generalizes Definitions 2 and 3
In the light of the work by Şeker [5], we investigate the coefficient problem for functions f ∈ A given by (1.1) belonging to the bi-univalent function class BΣm,n,γ (h, p) introduced in Definition 4 and give coefficient bounds on |a2| and |a3|
Summary
(w ∈ U) , Theorem 1.3 (see [5]) Let the function f (z) given by (1.1) be in the class Definition 4 Let the functions h, p : U → C satisfy the conditions min {R (h (z)) , R (p (z))} > 0 (z ∈ U) and h (0) = p (0) = 1.
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