A note on a certain subclass of analytic functions defined by multiplier transformation

In the present paper we define a new operator, by means of convolution product between Ruscheweyh operator and the multiplier transformation I (m, lambda, l). For functions f belonging to the class A we define the differential operator IR(lambda,l)(m) : A -> A, IR(lambda,l)(m) f(z) := (I (m, lambda, l) * R(m)) f (z) where 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 with A(1) = A. We study certain differential subordinations regarding the operator IR(lambda,l)(m).