On special differential superordinations using a generalized Sălăgean operator and Ruscheweyh derivative

In the present paper we establish several differential superordinations regarding the new operator RDn λ,α defined by using the generalized Sălăgean operator Dn λf (z) and Ruscheweyh derivative Rnf (z), RDn λ,α : A → A, RDn λ,α f (z) = (1 − α)Rnf (z) + αDn λf (z), z ∈ U, where n ∈ N, λ, α ≥ 0 and f ∈ A, A =  f ∈ H(U) : f (z) = z + ∞− j=2 ajzj, z ∈ U  . A number of interesting consequences of some of these superordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided.