Abstract
In the present paper we study the operator defined by using the Ruscheweyh derivative Rm f(z) and the Sălăgean operator Sm f(z), denoted Lmα : An → An, Lmα f(z) = (1−α)Rm f(z)+αSm f(z), z ∈ U, where An = {f ∈ H(U) : f(z) = z+an+1zn+1+. . . , z ∈ U} is the class of normalized analytic functions. We obtain several differential subordinations regarding the operator Lmα.