区域的Schwarz导数和对数导数单叶性内径  

THE UNIVALENT INNER RADIUS OF THE SCHWARZ DERIVATIVE AND PRE-SCHWARZ DERIVATIVE OF THE DOMAIN

作　　者：王朝川 杨敏 冯小高[1] WANG Chaochuan;YAN Min;FENG Xiaogao(College of Mathematic and Information,West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《井冈山大学学报（自然科学版）》2024年第5期1-8,共8页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11701459,12271218)。

摘　　要：利用Ahlfors所得关于解析函数单叶性与拟共形延拓的一般性公式,研究了单叶性内径问题。在角域和一般拟圆上得到Schwarz导数单叶性内径的几个下界估计公式。同时,在单位圆、上半平面、角域以及拟圆上,推广了对数导数单叶性内径的下界公式。The inner radius problem of univalence is studied by using the general formula of univalence and quasiconformal extension of analytic functions obtained by Ahlfors.We obtain several lower bounds for the inner radius of Schwarz derivative univalence on angular domain and general quasicircle.At the same time,on the unit circle,the upper half plane,the angular domain and the quasi-circle,the lower bound formula of the inner radius of the Pre-Schwarz derivative univalence is generalized.

关 键 词：单叶性内径 SCHWARZ导数 PRE-SCHWARZ导数 

分 类 号：O174.5[理学—数学]