涉及f'k-ak(z)fk2≠b(z)的正规性探讨
Discussion of Normality Involving f'k-ak(z)fk2≠b(z)
DOI: 10.12677/PM.2023.136189, PDF, HTML, 下载: 145  浏览: 215 
作者: 鲁凤年*, 杨锦华#：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 亚纯函数；正规定则；例外函数；Meromorphic Function； Normal Criterion； Omitted Function
摘要: 本文对涉及例外函数的正规定则进行了讨论，利用P -Z 引理和构造函数的方法，针对满足条件f'k-ak(z)fk2≠b(z)的一类亚纯函数族的正规性展开研究，我们得到a(z)(≢0),b(z) 为区域D内的两个全纯函数。当a(z)=0 时，f(z)≠∞且k≥4时,则F在D内正规。
Abstract: In this paper, the normal rules involving omitted functions are discussed, and the method of P 􀀀 Z lemma and constructor is used to study the normality of a class of meromorphic function family satisfying the condition (f(z)')k-ak(z)fk2≠b(z). We get thata(z)(≢0),b(z) are two holomorphic functios on D, and whenever a(z)=0, f(z)≠∞ andk≥4, the family of functions is normal.
文章引用：鲁凤年, 杨锦华. 涉及f'k-ak(z)fk2≠b(z)的正规性探讨[J]. 理论数学, 2023, 13(6): 1859-1866. https://doi.org/10.12677/PM.2023.136189

参考文献

[1] Yang, J.H., Yang, Q. and Pang, X.C. (2019) Normal Criterion of Meromorphic Functions. Acta Mathematica Sinica, English Series, 35, 1972-1978.
https://doi.org/10.1007/s10114-019-9058-1
[2] 陈鹏斌,杨祺. 涉及不取零点的亚纯函数族的正规性[J]. 龙岩学院学报,2023.41(2): 13-16.
[3] 陈鸿辉，蔡金华，袁文俊. 涉及零点与多项式的无零点亚纯函数族的正规性[J]. 西南师范大学学报，2018，43(8): 10-17.
[4] Yang, L. (1986) Normality for Families of Meromorphic Functions. Scientia Sinica, 9, 898-908.
[5] Deng, B.M., Fang, M.L. and Liu, D. (2011) Normal Families of Zero-Free Meromorphic Functions. Journal of the Australian Mathematical Society, 91, 313-322.
https://doi.org/10.1017/S1446788711001571
[6] 庞学诚.微分多项式的正规定则[J]. 科学通报，1988,33(22): 1690-1693.
[7] Pang, X.C. and Zalcman, L. (2000) Normality Families and Shared Values. Bulletin of the London Mathematical Society, 32, 325-331. https://doi.org/10.1112/S002460939900644X
[8] Pang, X.C., Nevo, S. and Zalcman, L. (2008) Derivatives of Meromorphic Functions with Multiple Zeros and Rational Functions. Computational Methods and Function Theory, 8, 483- 491.
https://doi.org/10.1007/BF03321700

为你推荐