In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)^β1z1,(rf(z1/r)/z1)^β2z2,...,(rf(z1/r)/z1)^βnzn)',where f is a normalized locall...In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)^β1z1,(rf(z1/r)/z1)^β2z2,...,(rf(z1/r)/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, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.展开更多
文摘In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)^β1z1,(rf(z1/r)/z1)^β2z2,...,(rf(z1/r)/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, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.