Hossein Piri

Let S ∗ Ωn,p2,...,pn (β, A, B) be some subclasses of starlike mappings on some Reinhardt domain Ωn,p2,...,pn = {z ∈ C n : |z1| 2 + Pn j=2 |zj | pj < 1}, where −1 ≤ A < B < 1 and β ∈ (− π 2 , π 2 ). Some different conditions for Q are established such that these classes are preserved under the following modified Roper-Suffridge operator [Φn,Q(f)](z) =  f(z1) + f 0 (z1)Q(ˆz), p f 0(z1)ˆz  , where f is a normalized biholomorphic function on the unit disc U, and (z1, zˆ) ∈ Ωn,p2,...,pn . Another conditions for Q are also obtained such that the above generalized Roper-Suffridge operator preserves a spirallike mapping of type β and order α and strongly spirallike mapping of type β and order α, respectively.