A NOTE ON DIFFERENTIAL SUPERORDINATIONS USING A MULTIPLIER TRANSFORMATION AND RUSCHEWEYH DERIVATIVE.

In the present paper we define a new operator, by means of convolution product between Ruscheweyh operator and the multiplier transformation I (m, λ, l). For functions f belonging to the class A_n we define the differential operator IR^m_λ,l : A_n → A_n, IR^m_λ,lf (z) := (I (m, λ, l) * R^m) f (z) , where A_n = {f ϵ H(U) : f(z) = z+a_n+1zⁿ⁺¹+…, z ϵ U} is the class of normalized analytic functions. We study some differential superordinations regarding the operator IR^m λ,l. [ABSTRACT FROM AUTHOR]