[1]赵小珍.亚纯函数及其导数分担小函数集的唯一性[J].江西师范大学学报(自然科学版),2012,(02):141-146.
 ZHAO Xiao-zhen.The Uniqueness of Meromorphic Functions and Their Derivatives Weighted-Sharing the Sets of Small Functions[J].,2012,(02):141-146.
点击复制

亚纯函数及其导数分担小函数集的唯一性()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年02期
页码:
141-146
栏目:
出版日期:
2012-03-01

文章信息/Info

Title:
The Uniqueness of Meromorphic Functions and Their Derivatives Weighted-Sharing the Sets of Small Functions
作者:
赵小珍
宁德师范学院数学系,福建宁德,352100
Author(s):
ZHAO Xiao-zhen
关键词:
亚纯函数弱权分担小函数唯一性
Keywords:
meromorphic function weakly weighted-sharing small function uniqueness
分类号:
O174.52
文献标志码:
A
摘要:
研究了亚纯函数及其k阶导数权分担小函数集的唯一性,得到了:设k,n为正整数,f,g为开平面上超越亚纯函数,以∞.为IM公共值,E(S,f)=E(S1,g)且E1(S2,f(k))=EI(S2,g(k)),f(≥2)∈N,如果2nδ2+k(an,,fn)+ (nk+ 4)(◎)(∞,f)>n(k+1)+4,则f≡tg(tn=1)或[(f(k))n-(a(k))n][(g(k))n-(a(k))n]≡[bn-(a(k))n]2,并且文中还讨论了当l=0,1时的情形.这些定理推广和改进了先前的一些结果.
Abstract:
The uniqueness of meromorphic functions and their derivatives weakly weighted-sharing the sets of small functions is investigated, and the following theorem is obtained. Let be two positive integers, f,g be nonconstant meromorphic functions in the complex plane C, f,g share and If 4, then or . Some results about in the above theorem are obtained in this paper. These theorems of this paper extend and improve the previous results.

参考文献/References:

[1] Hayman W K. Meromorphic functions [M].Oxford: Clarendon Press, 1964.
[2] Yi Hongxun, Yang Chungchun. Uniqueness theory of meromorphic functions [M]. Beijing: Science Press, 1995.
[3] 李江涛, 顾永兴. 亚纯函数及其导数的唯一性 [J]. 数学学报, 2000, 43(1): 87-94.
[4] Yang Chungchun. On two entire functions which together with their first derivatives have the same zeros [J]. J Math Anal App, 1976, 56: 1-6.
[5] Yi Hongxun. A question of C C Yang on uiqueness of entire functions [J]. Kodai Math J, 1990, 13: 39-46.
[6] Yuan Wenjun, Tian Honggen. Further results of some uiqueness theorems for meromorphic functions whose n-th derivatives share the same 1-points [J]. Advances in Applied Clifford Algebras, 2001, 11(S2): 317-325.
[7] Lin Shanhua, Lin Weichuai. Uniqueness of meromorphic functions concerning weakly weighted-sharing [J]. 2006, 29: 269- 280.
[8] 杨重俊, 仪洪勋. 具有亏值的亚纯函数的唯一性定理 [J]. 数学学报, 1994, 37(1): 62-72.
[9] 王金莲, 徐洪焱, 易才凤. 亚纯函数及其导数权分担两个值 [J]. 东北师大学报: 自然科学版, 2009, 41(4): 22-26.
[10] 方明亮. 亚纯函数及其导数的唯一性 [J]. 数学研究与评论, 1998, 18(3): 353-358.

相似文献/References:

[1]易才凤,李爱平.一类复合差分函数零点的估计[J].江西师范大学学报(自然科学版),2012,(01):41.
 YI Cai-feng,LI Ai-ping.The Estimate on Zeros of Composition Differences of Meromorphic Functions[J].,2012,(02):41.
[2]杨碧珑,易才凤.一类亚纯系数高阶线性微分方程解的增长性[J].江西师范大学学报(自然科学版),2012,(05):477.
 YANG Bi-long,YI Cai-feng.The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficient[J].,2012,(02):477.
[3]肖丽鹏,李明星.单位圆内非齐次线性微分方程的振荡解[J].江西师范大学学报(自然科学版),2013,(02):166.
 XIAO Li-peng,LI Ming-xing.Oscillatory Solutions of Nonhomogeneous Linear Differential Equation in the Unit Disc[J].,2013,(02):166.
[4]刘旭强,易才凤.关于2阶线性微分方程f″+Af'+Bf=0解的增长性[J].江西师范大学学报(自然科学版),2013,(02):171.
 LIU Xu-qiang,YI Cai-feng.On the Growth of Solutions of the Second Order Linear Differential Equation f"+Af'+Bf =0[J].,2013,(02):171.
[5]吴佳,吴芬,陈裕先.向量值亚纯函数的亏量[J].江西师范大学学报(自然科学版),2013,(03):229.
 WU Jia,WU fen,CHEN Yu-xian.Deficiency of Vector Valued Meromorphic Function[J].,2013,(02):229.
[6]涂金,黄海霞,徐洪焱,等.单位圆内亚纯函数与解析函数的级与型[J].江西师范大学学报(自然科学版),2013,(05):449.
 TU Jin,HUANG Hai-xia,XU Hong-yan,et al.The Order and Type of Meromorphic Functions and Analytic Functions in the Unit Disc[J].,2013,(02):449.
[7]何涛,易才凤.复振荡中的辐角分布[J].江西师范大学学报(自然科学版),2013,(05):453.
 HE Tao,YI Cai-feng.On Angular Distribution in Complex Oscillation[J].,2013,(02):453.
[8]陈雪,田宏根,袁文俊,等.涉及分担值的Lahiri型正规定理[J].江西师范大学学报(自然科学版),2014,(01):37.
 CHEN Xue,TIAN Hong-gen,YUAN Wen-jun,et al.Normality Criteria of Lahiri's Type Concerning Shared Values[J].,2014,(02):37.
[9]艾丽娟,易才凤.一类亚纯系数高阶线性微分方程解的增长性[J].江西师范大学学报(自然科学版),2014,(03):250.
 AI Li-juan,YI Cai-feng.The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficients[J].,2014,(02):250.
[10]杨碧珑,易才凤.一类高阶线性微分方程解在角域上的增长性[J].江西师范大学学报(自然科学版),2014,(04):390.
 YANG Bi-long,YI Cai-feng.The Growth of Solutions of a Class Higher Order Linear Differential Equations in Angular Donains[J].,2014,(02):390.

备注/Memo

备注/Memo:
福建省教育厅A类科技(JK2010062);福建省高校科研(JA11276);宁德师范学院重点课题(2010003)
更新日期/Last Update: 1900-01-01