On a certain subclass of analytic functions defined by a generalized S˘al˘agean operator and Ruscheweyh derivative

In the present paper we define a new operator using the generalized Sal˘ agean and Ruscheweyh operators. Denote by ˘ RDm λ,α the operator given by RDm λ,α : An → An, RDm λ,αf(z) = (1 − α)Rmf(z) + αDm λ f(z), z ∈ U, where Rmf(z) denote the Ruscheweyh derivative, Dm λ f(z) is the generalized Sal˘ agean operator and ˘ An = {f ∈ H(U) : f(z) = z +an+1z n+1 +. . . , z ∈ U} is the class of normalized analytic functions. A certain subclass, denoted by RDm (δ, λ, α) , of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class RDm (δ, λ, α) . Also, several differential subordinations are established regarding the operator RDm λ,α.