Normal families of meromorphic functions concerning shared values

被引：5

作者：

Ding, Jian-Jun ^{[1
]}

Ding, Li-Wei ^{[1
]}

Yuan, Wen-Jun ^{[1
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2013年 / 58卷 / 01期

关键词：

meromorphic function; normal family; shared values; DES VALEURS MULTIPLES; FONCTIONS ANALYTIQUES; CRITERIA; FAMILLES;

D O I：

10.1080/17476933.2011.555644

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we prove the following normality criterion: let n2, m, k be three positive integers, and a be a non-zero complex number. Let F be a family of meromorphic functions in a domain D such that each fF has only zeros of multiplicity at least max{k,2}. If for each pair of f and g in F, f(m)(f((k)))(n) and g(m)(g((k)))(n) share the value a IM, then F is normal in D. This extends Hu and Meng's result.

引用

页码：113 / 121

页数：9

共 21 条

[1]

Alotaibi A., 2004, Comput. Methods Funct. Theory, V4, P227, DOI [10.1007/BF03321066, DOI 10.1007/BF03321066]

[2]

[Anonymous], 1964, OXFORD MATH MONOGRAP

[3]

[Anonymous], 1978, SCI SINICA A

[4]

[Anonymous], ACTA MATH SIN

[5]

CHEN HH, 1995, SCI CHINA SER A, V38, P789

[6]

Hayman W. K., 1967, Research Problems in Function Theory

[7] Normality criteria of meromorphic functions with multiple zeros [J].

Hu, Pei-Chu ;

Meng, Da-Wei .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 357 (02) :323-329

[8]

[李国望 LI Guowang], 2008, [暨南大学学报. 自然科学与医学版, Journal of Jinan University], V29, P424

[9] On normal families of meromorphic functions [J].

Li, Yuntong ;

Gu, Yonping .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 354 (02) :421-425

[10] ON A TEST FOR THE NORMALITY OF FAMILIES OF HOLOMORPHIC-FUNCTIONS [J].

OSHKIN, IB .

RUSSIAN MATHEMATICAL SURVEYS, 1982, 37 (02) :237-238

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