In this paper, we study ε-starlike mappings on the unit ball in Cn, the upper bounds of coefficients of kth item of homogeneous expansion for ε-starlike mappings are obtained.
In this paper, the Alexander type theorem in several complex variables is given by using the parametric representation of a kind of starlike mappings. As a corollary, a new method is set up to prove that the Roper-Suffridge extension operator keeps the property of starlike.
Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s > N and any continuous v ∈∧(0,1)X L s, there exists a continuous u ∈ L s solving δbu = v.
In this paper, we construct a new Roper-Suffridge extension operator Φr n,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.
