In the present paper we study the operator RD lambda,alpha n f(z, zeta) defined by using the extended Ruscheweyh derivative R-n f(z, zeta) and the extended generalized Salagean operator D-lambda(n) f(z, zeta), as RD lambda,alpha n : A(zeta)* -> A(zeta)*, RD lambda,alpha n f (z, zeta) = (1 - alpha)R-n f(z, zeta) + alpha D-lambda(n) f(z, zeta), where A(n zeta)* = {f is an element of H(U x (U) over
... [Show full abstract] 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)*. We obtain several strong differential subordinations regarding the extended operator RD lambda,alpha n. Some examples are presented.