Univalence of the Integral of f ′(z) λ
Univalence of the Integral of f ′(z) λ
复制标题
f ′(z) λ 积分的单价性
DOI：
10.1112/blms/7.3.254
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发表时间：
1975
影响因子：
0.9
通讯作者：
J. Pfaltzgraff
中科院分区：
文献类型：
--
作者：
J. Pfaltzgraff
E={z：| z |< 1}则z= jf ′（w）x dw（1）在E中对所有复形X是单叶的，使得| X | ∈（幂是通过log i ′（w）的分支定义的，其中log i ′（0）= 0）。J. Becker [2]建立了（1）的单价，|一|和Royster已经在范围\X\^[8]中对每个络合物A# 1展示了非单价fx（z）（也参见[3]和[4]问题6.15）。因此，（1）的单价问题对于X在\<\X\^^范围内仍然是开放的。本文还完成了Robertson [7]提出的一个问题的求解。我们证明了如果f（z）= z+..是解析的，在E中是局部单叶的（f '（z）^ 0），如果
E={z:\z\< 1} then z= jf'(w) x dw(1) is univalent in E for all complex X such that\X\^£(tne power is defined via the branch of log/'(w) for which log/'(0)= 0). J. Becker [2] established univalence of (1) for| A|<£ and Royster has exhibited nonunivalent fx (z) for each complex A# 1 in the range\X\>^[8](see also [3] and [4] problem 6.15). Thus the question of univalence of (1) remains open for X in the range\<\X\^^. We also complete the solution of a problem posed by MS Robertson [7]. We show that if/(z)= z+... is analytic and locally univalent (f'(z)^ 0) in E and if