理论数学    Vol.7 No.6 (November 2017)

一个涉及分担集合的亚纯函数正规定则
A Normality Criterion of Meromorphic Functions Concerning Shared Set

作者: 厉珍珠 * , 雷春林 ：华南农业大学应用数学研究所，广东 广州;

关键词: 正规族； 亚纯函数； ZALCMAN引理； 分担集； Normal Families； Meromorphic Functions； Zalcman Lemma； Shared Set

摘要:
设 是区域D内的一族亚纯函数， a， b，c 是三个有穷复数并且 , k是正整数。令 。若对于任意的 满足：1) f-c的零点重级均 ；2) ，其中Dk(f)为f的线性微分多项式，则 在D内正规。

Abstract: Let be a family of meromorphic functions in a domain D, let a, b, c be finite complex numbers, and . Let k be a positive integer and . If, for each , the zeros of f-c are of multiplicity , and whenever , then is normal in D.

文章引用: 厉珍珠 , 雷春林 (2017) 一个涉及分担集合的亚纯函数正规定则。 理论数学， 7， 417-421. doi: 10.12677/PM.2017.76054

参考文献

[1] Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromorphic Function. Science Press/Kluwer Academic Publishers, Dordrecht, 1-70.
https://doi.org/10.1007/978-94-017-3626-8

[2] Hayman, W.K. (1964) Meromorphic Function. Clarendon Press, Oxford, 5-24.

[3] 顾永兴, 庞学诚, 方明亮. 正规族理论及其应用[M]. 北京: 科学出版社, 2007: 25-34.

[4] Schwick W. (1992) Sharing Values and Normality. Archiv der Mathematik, 59, 50-54.
https://doi.org/10.1007/BF01199014

[5] Chen, H.H. and Fang M.L. (2001) Shared Values and Normal Families of Meromorphic Functions. Journal of Mathematical Analysis and Applications, 260, 124-132.
https://doi.org/10.1006/jmaa.2001.7439

[6] Han, M.H. and Gu, Y.X. (2008) The Normal Famility of Mermorphic Function. Acta Mathematica Scientia, 28B, 759-762.

[7] Zalcman, L. (1998) Normal Families: New Perspective, Bull. American Mathematics Society, 35, 215-230.
https://doi.org/10.1090/S0273-0979-98-00755-1

[8] Wang, Y.F. and Fang, M.L. (1998) Picard Values and Normal Families of Meromorphic Functions with Multiple Zeros. Acta Mathematica Sinica, 14, 17-26.
https://doi.org/10.1007/BF02563879

[9] Fang, M.L. and Zalcman, L. (2003) Normal Families and Shared Values of Meromorphic Functions. Annales Polonice Mathematici, 80, 137-138.
https://doi.org/10.4064/ap80-0-11

分享
Top