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 RDλ,αn defined by using the generalized Sălăgean operator Dλnf(z) and Ruscheweyh derivative Rnf(z)Rnf(z), RDλ,αn:A→A, RDλ,αnf(z)=(1−α)Rnf(z)+αDλnf(z),z∈U, where n∈Nn∈N, λ,α≥0λ,α≥0 and f∈Af∈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.