Siberian Federal University

Let F(γ) κ,μ(ξ) = ξ + ∞∑ n=1 [ Γ(μ) Γ(κn + μ) ]γ ξn+1 be the normalized Le Roy-type Mittag-Leffler func- tion. The purpose of the present paper is to introduce two new subclasses Hγ Σ(κ, μ, λ, τ ) and Hγ Σ(κ, μ, λ, δ) of the function class Σ of bi-univalent functions defined by the function F(γ) κ,μ(ξ). Furthermore, we find estimates on the coefficients |a2| and |a3| for functions in these new subclasses. Also, we solve the Fekete–Szeg¨o functional problem for functions in the classes Hγ Σ(κ, μ, λ, τ ) and Hγ Σ(κ, μ, λ, δ). Several examples of the main results are also considered