Coefficient Estimates of some Classes of Rational Functions

Let A be the class of analytic and univalent functions in the open unit disc Δ normalized such that f ( 0 ) = 0 = f ′ ( 0 ) − 1. In this paper, for ψ ∈ A of the form z f ( z ) , f ( z ) = 1 + ∞ ∑ n = 1 a n z n and 0 ≤ α ≤ 1 , we introduce and investigate interesting subclasses H σ ( ϕ ) , S σ ( α , ϕ ) , M σ ( α , ϕ ) , I α ( α , ϕ ) and β α ( λ , ϕ ) ( λ ≥ 0 ) of analytic and bi-univalent Ma-Minda starlike and convex functions. Furthermore, we find estimates on the coefficients | a 1 | and | a 2 | for functions in these classess. Several related classes of functions are also considered.