劉克笑

(懷化學(xué)院預(yù)科部,湖南懷化 418008)

與分擔(dān)函數(shù)相關(guān)的亞純函數(shù)的正規(guī)性

劉克笑

(懷化學(xué)院預(yù)科部,湖南懷化 418008)

設(shè)為定義在區(qū)域D內(nèi)的一族亞純函數(shù),a(z)和b(z)為兩個(gè)在D滿足a(z)≠b(z)和a(z)≠b(k)(z)以及a(z)￠a′(z)的全純函數(shù),若對(duì)于任意的f∈,f(z)-a(z)的零點(diǎn)重級(jí)至少是k,f(z)和f(k)(z)分擔(dān)a(z),且當(dāng)f(z)=b(z)時(shí),f(k)(z)=b(z),那么在D內(nèi)正規(guī).

亞純函數(shù); 正規(guī)族; 分擔(dān)函數(shù)

1 引言及主要結(jié)論

3 定理的證明

這表明ξ0的個(gè)數(shù)是有限的即g(ξ)=0的零點(diǎn)是有限的,但從(9)可知g(ξ)=0有無(wú)限個(gè)零點(diǎn)1矛盾1

于是完成了定理的證明.

[1]Schiff.,Normal Families,New Y ork:Springer[M].1993.

[2]Montel P.,Sur les families de functions analytiques qui admettent des valeurs excptionnelles dans un domaine[J].Ann.E/cole Norm. Sup.,1912,29(3):478-535.

[3]Schwick W.Sharing values and normality[J].Arch.Math,1992,59:50-54.

[4]Pang X C.,Zalcman L.,Normality and shared values[J].Ark.Mat,2000,38:171-182.

[5]ChangJ.,Fang M.L.,ZalcmanL.,Normality andfixed-points of meromorphic functions[J].Ark.Mat.,2005,43:307-321.

[6]Pang X.C.,Zalcman L.,Normality and shared values[J].Bull.London Math.Soc.,2000,32:325-331.

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

Abstract:Letbe a familyof meromorphic functions on the plain domainD,a(z)andb(z)beholomorphic functions inD such thata(z)≠b(z)anda(z)≠b(k)(z)anda(z)￠a′(z)1If for everyf∈,the zeros off(z)-a(z)are of multiplicity at leastk,f(z)andf(k)(z)sharea(z),andf(z)=b(z)]f(k)(z)=b(z),thenis normal onD1

Key words:meromorphic function; normal family; shared function

Normal Families of Meromorphic Functions Concerning Shared Functions

LIU Ke-xiao
(Preparatory Department,Huaihua University,Huaihua,Hunan 418008)

O174152

A

1671-9743(2011)02-0011-05

2010-12-21

劉克笑(1973-),男,湖南辰溪人,懷化學(xué)院講師,碩士,主要研究復(fù)分析1