On special differential superordinations using a generalized Salagean operator and Ruscheweyh derivative

In the present paper we establish several differential superordinations regarding the new operator RD lambda,alpha n defined by using the generalized Salagean operator D(lambda)(n)f (z) and Ruscheweyh derivative R(n)f(z), RD lambda,alpha n : A -> A, RD(lambda,alpha)(n)f(z) = (1 - alpha)R(n)f(z) + alpha D(lambda)(n)f(z), z is an element of U, where n is an element of N, lambda, alpha >= 0 and f is an element of A, A = {f is an element of H(U) : f(z) = z + Sigma(infinity)(j=2)a(j)z(j), z is an element of U}. A number of interesting consequences of some of these superordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. (C) 2010 Elsevier Ltd. All rights reserved.