[1]李效敏,仪洪勋,张 学.涉及复合亚纯函数和不动点的亚纯函数的正规族[J].江西师范大学学报(自然科学版),2016,40(06):578-586.
 LI Xiaomin,YI Hongxun,ZHANG Xue.Normal Families of Meromorphic Functions Concerning Composite Meromorphic Functions and Fixed Points[J].,2016,40(06):578-586.
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涉及复合亚纯函数和不动点的亚纯函数的正规族()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年06期
页码:
578-586
栏目:
出版日期:
2016-12-01

文章信息/Info

Title:
Normal Families of Meromorphic Functions Concerning Composite Meromorphic Functions and Fixed Points
作者:
李效敏仪洪勋张 学
1.中国海洋大学数学科学学院,山东 青岛 266100; 2.山东大学数学学院,山东 济南 250199
Author(s):
LI XiaominYI HongxunZHANG Xue
1.Department of Mathematics,Ocean University of China,Qingdao Shandong 266100,China; 2.Department of Mathematics,Shandong University,Jinan Shandong 250199,China
关键词:
亚纯函数 复合函数 不动点 分担值 正规定则
Keywords:
meromorphic functions composite functions fixed-points shared values normal criterions
分类号:
O 174.52
摘要:
假设f是一个超越整函数,G是定义在区域DC上的全纯函数族. 如果对G中每个元素g,f(g)-α1在区域D上的每个零点重数≥2,f(g)-α2和g-α2在区域D上IM分担0, 这里α1和α2是2个判别的有穷复数,则G在区域D上是正规的,该结果推广了Bergweiler 2004年的一个结果.同时还证明了: 假设R 是一个次数满足deg R≥2(deg R≥3,并且R在在复平面上有3个判别的有限的不动点)的有理函数,F是一个定义在区域DC上的全纯函数(亚纯函数),并且对F中每个元素f,Rf(z)-z 和f(z)-z在区域D上IM分担0,则F是区域D上的正规族, 该结果推广了方明亮与袁文俊2000年的一个结果, 也推广了常建明、方明亮与L.Zalcman 2005年的一个结果, 并举例说明本文结果从某种意义上来讲是最佳的.
Abstract:
Then following result is proved: If f is a transcendental entire function, such that the family G of all functions g holomorphic in the domain DC for which every zero of f(g)-α1 is of multiplicity ≥2,f(g)-α2 and g-α2 share 0 IM in D, where α1 and α2 are two distinct finite values, then G is normal in D. This result extends Theorem 1 of paper in Bergweiler.The following result is also proved: If R is a rational function with degR≥2(respectively ≥3, and R has three distinct finite fixed points in the complex plane)such that the family F of all functions f holomorphic(respectively meromorphic)in the domain DC for which R f(z)-z and f(z)-z share 0 IM in D, then F is normal in D. The results extend the corresponding results due to Fang-Yuan and Chang-Fang-Zalcman respectively. Examples are provided to show that the main results in this paper, in a sense, are the best possible.

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备注/Memo

备注/Memo:
收稿日期:2016-10-10基金项目:国家自然科学基金(11171184,11461042)和山东省自然科学基金(Z2008A01,ZR2014AM011)资助项目.作者简介:李效敏(1967-),男,山东莱芜人,教授,主要从事复分析研究.
更新日期/Last Update: 1900-01-01