王曉晶

(淮陰師范學(xué)院數(shù)學(xué)科學(xué)學(xué)院,江蘇淮安 223300)

分擔(dān)值與正規(guī)族

王曉晶

(淮陰師范學(xué)院數(shù)學(xué)科學(xué)學(xué)院,江蘇淮安 223300)

討論了涉及分擔(dān)值的全純函數(shù)族的正規(guī)性問(wèn)題.利用Zalcman引理,證明了全純函數(shù)族的幾個(gè)正規(guī)定則,推廣了Miranda定理.

正規(guī)族;分擔(dān)值;全純函數(shù)

0 引言及主要結(jié)論

1 幾個(gè)引理

2 定理1的證明

[1] Pang X.Shared values and normal families[J].Analysis,2002,22:175-182.

[2] Chen H,Hua X.Normal families concerning shared values[J].Israel JMath,2000,115:355-362.

[3] Pang X,Zalcman L.Normal families and shared values[J].Bull London Math Soc,2000,32:325-331.

[4] Chang J,Fang M,Zalcman L.Normal familiesof holomorphic functions[J].Illinois JMath,2004,48:319-337.

[5] Clunie J,Hayman W.The spherical derivative of integral and meromorphic functions[J].Comment Math Helv,1966,40:117-148.

Abstract:In this article,we discuss normality criteriaof holomorphic functions concerning shared values.By using Zalcman lemma,weobtain some normal criterionsof holomorphic functions in a simpleway.Which improve and generalize the Miranda criterion.

Key words:shared value;normal family;holomorphic functions

[責(zé)任編輯:李春紅]

Shared Values and Normal Fam ily

WANGXiao-jing

(School of Mathematical Science,Huaiyin Normal University,Huaian Jiangsu 223300,China)

O174.52

A

1671-6876(2010)06-0476-02

2010-09-12

王曉晶(1974-),男,江蘇東臺(tái)人,講師,碩士,研究方向?yàn)閺?fù)分析與微分方程.