In this note, the author introduces some new subclasses of starlike mappings
S*Ωn, p2,···, pn( β, A, B)
={f ∈H(Ω) : | i tan β+ (1 − i tanβ ) 2/ρ(z) ∂ρ/∂z (z)J−1f (z)f(z) − 1 − AB/1 − B2 |< B − A/1 − B2},
on Reinhardt domains Ωn, p2,···, pn= {z ∈ Cn : |z1|2+∑nj=2|zj |pj < 1}, where −1 ≤ A < B <1, q = min{p2, · · · , pn} ≥ 1, l = max{p2, · · · , pn} ≥ 2 and β ∈ (−π/2 , π/2 ). Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator
F(z) =（f(z1) + f′(z1)Pm(z0), (f′(z1)1/m z0）′,
where f is a normalized biholomorphic function on the unit disc D, z = (z1, z0) ∈Ωn, p2,···, pn, z0 = (z2, · · · , zn) ∈Cn−1. Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type and order . These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 = · · · = pn = 2, our results reduce to the recent results of Feng and Yu.
