A new roper-suffridge extension operator on bounded complete reinhardt domains

In this paper, we construct a new Roper-Suffridge extension operator Φn,β1,…βnr(f)(z)=F(z)=((rf(z1r)z1)β1z1,(rf(z1r)z1)β2z2,…,(rf(z1r)z1)βnzn)′,where f   is a normalized locally biholomorphic function on the unit disc D, r=sup{|z1|:z=(z1,…,zn)∈Ω},β1∈[0,1],0≤βk≤β1,k=2,…,n,D, r=sup{|z1|:z=(z1,…,zn)∈Ω},β1∈[0,1],0≤βk≤β1,k=2,…,n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of order α on bounded complete Reinhardt domain Ω, respectively.