On the normal meromorphic functions

被引:1
作者
Zhu, Rongping [1 ]
Xu, Yan [2 ]
机构
[1] Jiangsu Univ, Dept Math, Jiangsu 212003, Zhenjiang, Peoples R China
[2] Nanjing Normal Univ, Dept Math, Nanjing 210097, Peoples R China
关键词
meromorphic function; normal family; normal function; uniformly normal family;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let F be a family of functions meromorphic in D such that all the zeros of f is an element of T are of multiplicity at least k (a positive integer), and let E be a set containing k + 4 points of the extended complex plane. If, for each function f is an element of F, there exists a constant M and such that (1 - |z|(2))(k) |f((k))(Z)|/(1+ |f (z)|(k+1))<= M whenever z is an element of {f (z)is an element of E, z is an element of D}, then F is a uniformly normal family in D, that is, sup{(1-|z|(2))f(#) (z) : z is an element of D, f is an element of F} < infinity.
引用
收藏
页码:129 / 133
页数:5
相关论文
共 8 条
[1]  
Hayman W K., 1964, MEROMORPHIC FUNCTION
[2]   PICARD VALUES OF MEROMORPHIC FUNCTIONS AND THEIR DERIVATIVES [J].
HAYMAN, WK .
ANNALS OF MATHEMATICS, 1959, 70 (01) :9-42
[3]  
Lappan P., 1977, ANN ACAD SCI FENN-M, V3, P301
[4]   BOUNDARY BEHAVIOUR AND NORMAL MEROMORPHIC FUNCTIONS [J].
LEHTO, O ;
VIRTANEN, KI .
ACTA MATHEMATICA, 1957, 97 (1-2) :47-65
[5]  
Pang XC, 2000, CHINESE ANN MATH, V21, P601
[6]   Normal functions and α-normal functions [J].
Yan, X .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2000, 16 (03) :399-404
[7]  
Yang L., 1993, VALUE DISTRIBUTION T
[8]   HEURISTIC PRINCIPLE IN COMPLEX FUNCTION THEORY [J].
ZALCMAN, L .
AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (08) :813-817