Differential subordinations using ruscheweyh derivative and S?l?gean operator

Abstract

In the present paper we study the operator defined by using the Ruscheweyh derivative Rm f(z) and the S?l?gean operator Sm f(z), denoted Lm? : An ? An, Lm? f(z) = (1??)Rm f(z)+?Sm 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 Lm?.