Properties on a subclass of univalent functions defined by using a multiplier transformation and Ruscheweyh derivative

In this paper we have introduced and studied the subclass RI(d, α, β) of univalent functions defined by the linear operator RI n,λ,lf(z) defined by using the Ruscheweyh derivative Rf(z) and multiplier transformation I (n, λ, l) f(z), as RI n,λ,l : A → A, RI γ n,λ,lf(z) = (1 − γ)R f(z) + γI (n, λ, l) f(z), z ∈ U, where An = {f ∈ H(U) : f(z) = z+ an+1z + . . . , z ∈ U} is the class of normalized analytic functions with A1 = A. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class RI(d, α, β).