Coefficient estimates for some subclasses of bi-univalent functions

Let A be a class of functions of the form f ( z ) = z + ∑ n = 2 ∞ a n z n which are analytic in the open unit disc D = { z ∈ ℂ : | z | < 1 } where a n is a complex number. Also let S denotes a subclass of all functions in A which are univalent in D and let Σ denotes the class of bi-univalent functions in D. In this paper, we introduce two subclasses of Σ defined in the open unit disk D which are denoted by G ∑ s ( α , β ) and G * ∑ s ( α , β ) and we find the upper bounds for the second and S LS third coefficients for functions in these subclasses.