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具有公共值微分多项式的唯一性
The Uniqueness of Differential Polynomials Sharing Two Values
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禚彩萍, 王赞春, 李秋颖
Pure Mathematics (PM) , 2013, DOI: 10.12677/PM.2013.36056
Abstract:
本文研究了亚纯函数的微分多项式分担两个值的唯一性问题。利用重数的概念,得到了两个定理,其结果推广了前人的有关定理。
This paper is devoted to studying the uniqueness problem on meromorphic functions whose dif- ferential polynomials share two values. By using the notion of multiplicity, we obtain two theorems which improve the previous results.
亚纯函数与微分多项式分担小函数的唯一性
Uniqueness of Meromorphic Function and Its Differential Polynomial Sharing Small Functions
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杨城威, 刘丹
Pure Mathematics (PM) , 2015, DOI: 10.12677/PM.2015.55030
Abstract:
本文研究了亚纯函数及其微分多项式分担两个小函数的唯一性定理,证明了:设f(z)是开平面上满足\"\" 的非常数亚纯函数,n是正整数,a(z)和b(z)为f(z)的两个相互判别的小函数,\"\" ,其中\"\"f(z)的小函数。若f(z)和F(z)几乎CM分担a(z)b(z),则\"\"。这个结果改进了已有的一些结果。
In this paper, we study the uniqueness of meromorphic function and its differential polynomial sharing two small functions, and prove the follow theory. Let f(z) be a nonconstant meromor-phic function satisfying\"\", let n be an integer and let a(z) and b(z) be two distinct small functions related to f(z) . Let\"\", where \"\"are small functions related to f(z) . If f(z) and F(z) share a(z) and b(z) CM almost, then
亚纯函数微分多项式分担两个值的唯一性
Uniqueness of Meromorphic Function of Differential Polynomials Sharing Two Values
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石新华
Pure Mathematics (PM) , 2014, DOI: 10.12677/PM.2014.42011
Abstract:
本文运用Nevanlinna理论讨论了一类亚纯函数微分多项式分担两个值的唯一性问题,得到的结果改进或推广了亚纯函数分担值的许多唯一性结果。
We will use Nevanlinna distribution theory to discuss a power of meromorphic functions of differential polynomials sharing two values. The results generalize many results on value sharing of meromorphic functions.
具有权弱分担值的差分或微分多项式的亚纯函数的唯一性
The uniqueness of meromorphic functions of the differential or differential polynomial with the weakly weighed sharing value
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林珊华,林伟川
福州大学学报(自然科学版) , 2018, DOI: 10.7631/issn.1000-2243.16270
Abstract: 利用权弱分担的定义以及唯一性理论方法讨论亚纯函数的k阶导数与差分或微分多项式的k阶导数分担值的问题. 分析结果表明,当分担“(1,m)”且Θ(∞,f)介于一定范围的情况下,两个函数的k阶导数相等,其中对应不同的m值,n,m需满足不同的不等式.
We mainly use the definition of the weakly weighted sharing and the theory of uniqueness to discuss the problem that the k derivative of meromorphic function and the k derivative of the differential or differential polynomial share one value. The result is that k derivative of the two functions are equal when they share “(1,m)” and Θ(∞,f) is in a certain range,and different m value needs to satisfy different inequalities
The Uniqueness of Analytic Functions on Annuli Sharing Some Values
Hong-Yan Xu,Zu-Xing Xuan
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/896596
Abstract: The purpose of this paper is to deal with the shared values and uniqueness of analytic functions on annulus. Two theorems about analytic functions on annulus sharing four distinct values are obtained, and these theorems are improvement of the results given by Cao and Yi.
Generalization of Uniqueness of Meromorphic Functions Sharing Fixed Point  [PDF]
Harina P. Waghamore, Sangeetha Anand
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.79084
Abstract: In this paper, we study the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing fixed point and obtain some results which generalize the results due to Subhas S. Bhoosnurmath and Veena L. Pujari [1].
Multiple values and uniqueness problem of meromorphic mappings sharing hypersurfaces  [PDF]
Ting-Bin Cao,Hong-Zhe Cao
Mathematics , 2013,
Abstract: The purpose of this article is to deal with the multiple values and uniqueness problem of meromorphic mappings from $\mathbb{C}^{m}$ into the complex projective space $\mathbb{P}^{n}(\mathbb{C})$ sharing fixed and moving hypersurfaces. We obtain several uniqueness theorems which improve and extend some known results.
Some Uniqueness Results On Meromorphic Functions Sharing Three Sets II
Banerjee,Abhijit;
Cubo (Temuco) , 2011, DOI: 10.4067/S0719-06462011000300004
Abstract: with the help of the notion of weighted sharing we investigate the uniqueness of meromorphic functions concerning three set sharing and significantly improve two results of zhang [16] and as a corollary of the main result we improve a result of the present author [2] as well.
Uniqueness of meromorphic functions sharing two sets with finite weight ii
Abhijit Banerjee
Tamkang Journal of Mathematics , 2010, DOI: 10.5556/j.tkjm.41.2010.379-392
Abstract: With the help of the notion of weighted sharing of sets we deal with the well known question of Gross and prove some uniqueness theorems on meromorphic functions sharing two sets. Our results will improve and supplement some recent results of the present author.
Weakly Weighted Sharing and Uniqueness of Meromorphic Functions  [PDF]
Thamir Alzahary
Journal of Complex Analysis , 2014, DOI: 10.1155/2014/378958
Abstract: With the aid of the notion of weakly weighted sharing, we study the uniqueness of meromorphic functions sharing four pairs of small functions. Our results improve and generalize some results given by Czubiak and Gundersen, Li and Yang, and other authors. 1. Introduction and Main Results In this paper, a meromorphic function means meromorphic in the whole complex plane . We assume the reader is familiar with the standard notion used in the Nevanlinna value distribution theory such as , , , and (see [1, 2]). For any nonconstant meromorphic function , the term denotes any quantity that satisfies as outside a possible exceptional set of finite linear measure. Let be a nonconstant meromorphic function. A meromorphic function is called a small function of , if . If is a positive integer, we denote by the reduced counting function of the poles of whose multiplicities are less than or equal to and denote by the reduced counting function of the poles of whose multiplicities are greater than or equal to . Let and be nonconstant meromorphic functions, and let , be two values in . We say that and share the value IM provided that and have the same zeros ignoring multiplicities. In addition, we say that and share the value IM, if and share IM. We say that and share the pair of values IM provided that and have the same zeros ignoring multiplicities. The following theorem is a well-known and significant result in the uniqueness theory of meromorphic functions and has been proved by Czubiak and Gundersen. Theorem A (see [3]). Let and be two nonconstant meromorphic functions that share six pairs of values , IM, where whenever and whenever . Then is a M?bius transformation of . The following example, found by Gundersen, shows that the number “six” in Theorem A cannot be replaced with “five.” Example 1 (see [4]). Let , . We see that , share , , , and IM, and is not a M?bius transformation of . Let and be nonconstant meromorphic functions and let be two small meromorphic functions of and . We denote by the reduced counting function of the common zeros of and . We say that and share , if As in Theorem A and throughout this paper, when and are nonconstant meromorphic functions, we let denote the term which is both and simultaneously. We denote by the reduced counting function of those -points of , which are not the -points of . We note that and share if and only if and . According to this note, we generalize the definitions of IM and to the weakly weighted IM sharing which is given by the following definition. Definition 2 (see [5]). Let be a positive integer or infinity, and
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