On Convex Univalent Functions
On Convex Univalent Functions
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关于凸单价函数
DOI：
10.1112/jlms/s2-1.1.483
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发表时间：
1969
影响因子：
1.2
通讯作者：
T. Sheil‐Small
中科院分区：
文献类型：
--
作者：
T. Sheil‐Small
下面的结果是众所周知的。定理A. 7/ | /(z) | < iWT /或|s| < 1，则对于所有n和\z\ < 1，则\(rn(z)\ < M。反过来，如果\an(z)\ < M对于所有n和\z\ < 1，则\f(z)\ < M定理b如果\f(z)\ < M对于\z\ < 1，则\sn(z)\ < M对于所有n和\z\ <。这个数字\是最好的。定理A的证明（例如，参见[6，pp. 235-236]）依赖于以下事实：Kn(r, 0) >对于r < 1和(2)CKn(-, 4) d4> = 1, (3) limoi,(z) = / (s)；定理B的证明（例如，参见[6，pp. 235-236]）由性质kn(r, 6) > 0 （r < I）和I kn(, <M d<j> = 1， IT j \ p /获1968年10月23日。这项研究得到了美国国家科学基金会GP-8225拨款的支持。123
7T «/ o \ p / The following results are well known. THEOREM A. 7/ | /(z) | < iWT /or |s| < 1, then \(rn(z)\ < M for all n and \z\ < 1. Conversely, if \an(z)\ < M for all n and \z\ < 1, then \f(z)\ < M. THEOREM B. If \f(z)\ < M for \z\ < 1, then \sn(z)\ < M for all n and \z\ < \. The number \ is best possible. The proof of Theorem A (see, for example, [6, pp. 235-236]) depends on the facts that Kn(r, 0) > 0 for r < 1 and (2) CKn(-, 4) d4> = 1, (3) limoi,(z) = / ( s ) ; the proof of Theorem B (see, for example, [6, pp. 235-236]) follows in a similar way from the properties kn(r, 6) > 0 (r < I) and I kn(, <M d<j> = 1, IT Jo \ p / Received October 23, 1968. This research was supported by the National Science Foundation under Grant GP-8225. 123