Differential subordinations using the Ruscheweyh derivative and the generalized Salagean operator

In the present paper, we study the operator, using the Ruscheweyh derivative R(m)f(z) and the generalized Salagean operator D(lambda)(m)f(z), denote by RD lambda,alpha m : A(n) -> A(n), RD lambda,alpha m f(z) = (1 - alpha) R-m f(z) + alpha D-lambda(m) f(z), z epsilon U, where An = {f epsilon H(U) : f(z) = z + a(n+1)z(n+1) + ... , z epsilon U} is the class of normalized analytic functions. We obtain several differential subordinations regarding the operator RD lambda,alpha m