The generalized Roper–Suffridge extension operator for some biholomorphic mappings

Suppose f is a spirallike function of type β (or starlike function of order α) on the unit disk D   in CC. Let Ωn,p1,p2,…,pn={z=(z1,z2,…,zn)′∈Cn:∑j=1n|zj|pj<1}, where 1⩽p1⩽21⩽p1⩽2 (or 0