Abstract
In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a2 and a3 for functions of these subclasses. We discuss the improved results for the associated classes involving many of the new and well-known consequences. We notice that there is symmetry in the results obtained for the new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ, as there is a symmetry for the estimations of the coefficients a2 and a3 for all the subclasses defind in our this paper.
Highlights
In [17,19] Brannan and Taha get initial coefficient bounds for subclasses of bi-univalent functions
Let H be the class of analytic functions f defined in the open unit disk U = {z : |z| < 1} and normalized by conditions f (0) = 0, f (0) = 1
A function f ∈ H is said to be in the class RμΣ,αb,c(λ, δ, τ, Φ), 0 ≤ λ ≤ 1, 0 ≤ δ ≤ 1, and τ∈ C\{0}, if the following quasi-subordinations hold
Summary
In [17,19] Brannan and Taha get initial coefficient bounds for subclasses of bi-univalent functions. Srivastava et al [20] introduced and investigated subclasses of bi-univalent functions and get bounds for the initial coefficients.
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