The rotation theorem for starlike univalent functions
The rotation theorem for starlike univalent functions
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星状单价函数的旋转定理
DOI：
10.1090/s0002-9939-1953-0053221-5
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发表时间：
1953
期刊：
影响因子：
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通讯作者：
A. Goodman
中科院分区：
文献类型：
--
作者：
A. Goodman
其仅在r>> 1的极限中是尖锐的。Stroganoff [8]证明了对于z/（l-z）2形式的函数，对于适当的z值，可以得到Pi的精确界，但他的证明相当长和复杂。在§2中，我们将给出这个结果的一个证明，它比Stroganoff给出的证明既短又简单。Birnbaum [3]得到了P2和T2的上界。在§3中，我们得到了T2的sharp界和P2的一个改进的界，并且我们的方法揭示了求sharp界的困难
which is sharp only in the limit as r—»1. Stroganoff [8] proved that the sharp bound for Pi is attained for a function of the form z/(l —z)2 for an appropriate value of z, but his proof is rather long and complicated. In §2 we shall present a proof of this result, which is both shorter and simpler than the one given by Stroganoff. Birnbaum [3] obtained upper bounds for P2 and T2. In §3 we obtain the sharp bound for T2, and an improved bound for P2, and our method brings to light the difficulty of finding the sharp bound