Coefficient estimates for some subclasses of bi-univalent functions

Abstract

Let A be a class of functions of the form f(z)=z+∑n=2∞anzn which are analytic in the open unit disc D={ z∈ℂ:| z |<1 } where an 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.