On special strong differential subordinations using Saldgean and Ruscheweyh operators

In the present paper we establish several strong differential subordinations regardind the new operator L-a(n), given by L-a(n) : A(zeta)* -> A(zeta)*, L-a(n) f(z, zeta) = (1 - alpha) R-n f (z, zeta) + alpha S-n f(z, zeta), where R-n f (z, zeta) denote the Ruscheweyh derivative, S-n f (z, zeta) is the Salagean operator and A(n zeta)* = {f is an element of H(U x (U) over bar), f(z, zeta) = z + a(n+1) (zeta) z(n+1) + ..., z is an element of U, zeta is an element of (U) over bar} is the class of normalized analytic functions with A(1 zeta)* = A(zeta)*.