开拓劳宾生和戈鲁辛的几个定理

任福尧

数学学报 ›› 1958, Vol. 8 ›› Issue (2) : 181-189.

数学学报 ›› 1958, Vol. 8 ›› Issue (2) : 181-189. DOI: 10.12386/A1958sxxb0012
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开拓劳宾生和戈鲁辛的几个定理

    任福尧
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EXTENSIONS OF SOME THEOREMS OF ROBINSON AND GOLUSIN

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<正> 1.设 p 次对称函数(?)在单位圆|z|<1中是正则的单叶的,此种函数的全体成一函数族 S_p.当p=1时,简讯 S_1为 S.设ω=f(z)∈S_p 映照|z|<1于 W 面上时,其像关于原点成星形,此种 f(z)成 S_p 之一子族S_p.设 f(z)∈S_p,

Abstract

1.Let the p-symmetric function(?)schlicht in the unit circle |z|<1.The totality of all such functions forms aclass which shall be denoted by S_p.For brevity we denote S_1 by S.Let S_pbe the subclass of S_p consisting of all functions W=f(z)of S_p which map|z|<1 onto regions star-shaped with respect to W=0.Supposing f(z)∈S_p,there exists an x=x(f,z),01,and obtain thefollowing precise estimations.(a)Suppose f(z)∈S_p,|z|<1,then(?)where x is determind by(1)or(2).(b)If:0

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任福尧. 开拓劳宾生和戈鲁辛的几个定理. 数学学报, 1958, 8(2): 181-189 https://doi.org/10.12386/A1958sxxb0012
EXTENSIONS OF SOME THEOREMS OF ROBINSON AND GOLUSIN. Acta Mathematica Sinica, Chinese Series, 1958, 8(2): 181-189 https://doi.org/10.12386/A1958sxxb0012

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