On a certain subclass of analytic functions defined by a generalized Salagean operator and Ruscheweyh derivative

In the present paper we define a new operator using the generalized Salagean and Ruscheweyh operators. Denote by RD lambda,alpha m the operator given 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 is an element of U, where R-m f(z) denote the Ruscheweyh derivative, D-lambda(m) f (z) is the generalized Salagean operator and A(n) = {f is an element of H(U) : f(z) = z + a(n+1) z(n+1) + ..., z is an element of U} is the class of normalized analytic functions. A certain subclass, denoted by RDm (delta, lambda, alpha), of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class RDm (delta, lambda, alpha). Also, several differential subordinations are established regarding the operator RD lambda,alpha m.