Coefficient Estimates of some Classes of Rational Functions

Abstract

Let A be the class of analytic and univalent functions in the open unit disc ∆ 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 anz n and 0 ≤ α ≤ 1, we introduce and investigate interesting subclasses Hσ(φ), Sσ(α, φ), Mσ(α, φ), =α(α, φ) and βα(λ, φ) (λ ≥ 0) of analytic and bi-univalent Ma-Minda starlike and convex functions. Furthermore, we find estimates on the coefficients |a1| and |a2| for functions in these classess. Several related classes of functions are also considered. Mathematics Subject Classification: 30C45.