Certain special differential superordinations using multiplier transformation and Ruscheweyh derivative
In the present paper we establish several differential superordinations regardind the new operator RI(m,lambda,l)(alpha) defined by using the multiplier transformation I (m, lambda, l) f (z) and R.uscheweyh derivative R(m) f (z), RI(m,lambda,l)(alpha) : A(n) -> A(n), RI(m,lambda,l)(alpha)f(z) = (1 - alpha)R(m) f (z) + alpha I (m, lambda, l) f (z), z is an element of U, where m, n is an element of N, lambda, alpha, l >= 0 and f is an element of A(n) = {f is an element of H(U) : f(z) = z + Sigma(infinity)(j=n+1) a(j)z(j), z is an element of U}. A number of interesting consequences of sonic 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.
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