Differential subordinations using ruscheweyh derivative and Sălăgean operator

Abstract

In the present paper we study the operator defined by using the Ruscheweyh derivative Rmf(z) and the Sălăgean operator Smf(z), denoted Lmα : An → An, Lmα f(z) = (1−α)Rmf(z)+αSmf(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 .