CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS SATISFYING SUBORDINATE CONDITIONS

In this paper, we introduce and investigate each of the following subclasses: SΣ(λ,γ;ϕ), HS Σ(α), RΣ(η,γ;ϕ) and BΣ(μ;ϕ) (0 λ 1; γ ∈ C� {0}; α ∈ C ;0 η 0, and ϕ(D) is symmetric with respect to the real axis. We obtain coefficient bounds involving the Taylor-Maclaurin coefficients |a2| and |a3| of the function f when f is in these classes. The various results, which are presented in this paper, would generalize and improve those in related works of several earlier authors.