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Uniqueness of meromorphic functions concerning differential polynomials
Subhas S. Bhoosnurmath,Veena L. Pujari,Anupama J. Patil
Tamkang Journal of Mathematics , 2012, DOI: 10.5556/j.tkjm.43.2012.51-68
Abstract: In this paper, we present a different and very simple technique to handle various uniqueness problems involving three small entire functions. It also gives a new additional insight into such problems.
Unicity of meromorphic functions concerning differential equation  [cached]
Subhas S. Bhoosnurmath,Milind N. Kulkarni,Vaishali Prabhu
Tamkang Journal of Mathematics , 2007, DOI: 10.5556/j.tkjm.38.2007.153-157
Abstract: In this paper,we investigate the uniqueness of meromorphic function satisfying a differential equation. Our result improves some known results.
UNIQUENESS OF MEROMORPHIC OR ENTIRE FUNCTIONS AND THEIR DIFFERENTIAL POLYNOMIALS
Li Jiangtao,Li Chunghong,
李江涛
,李纯红

数学物理学报(A辑) , 2006,
Abstract: This article studies the problem of uniqueness of two entire or meromorphic functions whose differential polynomials share a finite set. The results extendand improve on some theorems given in 3].
Uniqueness of Meromorphic Functions and Differential Polynomials  [PDF]
Jin-Dong Li
International Journal of Mathematics and Mathematical Sciences , 2011, DOI: 10.1155/2011/514218
Abstract: We study the uniqueness of meromorphic functions and differential polynomials sharing one value with weight and prove two main theorems which generalize and improve some results earlier given by M. L. Fang, S. S. Bhoosnurmath and R. S. Dyavanal, and so forth. 1. Introduction and Results Let be a nonconstant meromorphic function defined in the whole complex plane . It is assumed that the reader is familiar with the notations of the Nevanlinna theory such as , , , and , that can be found, for instance, in [1–3]. Let and be two nonconstant meromorphic functions. Let be a finite complex number. We say that and share the value CM (counting multiplicities) if and have the same zeros with the same multiplicities, and we say that and share the value IM (ignoring multiplicities) if we do not consider the multiplicities. When and share 1 IM, let be a 1-point of of order and a 1-points of of order ; we denote by the counting function of those 1-points of and , where and by the counting function of those 1-points of and , where . is the counting function of those 1-points of both and , where . In the same way, we can define , , and . If and share 1 IM, it is easy to see that Let be a nonconstant meromorphic function. Let be a finite complex number and a positive integer; we denote by (or ) the counting function for zeros of with multiplicity (ignoring multiplicities) and by (or ) the counting function for zeros of with multiplicity at least (ignoring multiplicities). Set We further define In 2002, C. Y. Fang and M. L. Fang [4] proved the following result. Theorem A (see [4]). Let and be two nonconstant entire functions, and let (≥8) be a positive integer. If and share 1 CM, then . Fang [5] proved the following result. Theorem B (see [5]). Let and be two nonconstant entire functions, and let , be two positive integers with . If and share 1 CM, then . In [6], for some general differential polynomials such as , Liu proved the following result. Theorem C (see [6]). Let and be two nonconstant entire functions, and let be three positive integers such that . If and share 1 IM, then either or and satisfy the algebraic equation , where . The following example shows that Theorem A is not valid when and are two meromorphic functions. Example 1.1. Let , , where . Then and share 1 CM, but . Lin and Yi [7] and Bhoosnurmath and Dyavanal [8] generalized the above results and obtained the following results. Theorem D (see [7]). Let and be two nonconstant meromorphic functions with , and let be a positive integer. If and share 1 CM, then . Theorem E (see [8]). Let and be two
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].
Uniqueness Theorems for Meromorphic Functions Concerning Fixed-points  [PDF]
WU Chun
Journal of Chongqing Normal University , 2009,
Abstract: In this article, we deal with the uniqueness problems on meromorphic functions conceming differential polynomials that share fixed-points, and we prove:if f, g be two nonconstant entire function and n(>4m+11)be a positive integer. If fn(fm-1)f' and gn(gm-1)g' share z IM, then f≡g; if f, g be two nonconstant meromorphic function and n(>4m+22)be a positive integer. If fn(fm-1)f' and gn(gm-1)g' share z IM, then f≡g, or gm=(m+n+1)/(n+1)*(1-hn+1)/(1-hn+m+1,fm=(m+n+1)/(n+1)*((1-hn+1)*hm)/(1=hn+m+1) here h(z) be a nonconstant meromorphic function. Moreover, we greatly improve the former result.
Uniqueness of Transcendental Meromorphic Functions with Their Nonlinear Differential Polynomials Sharing the Small Function  [PDF]
Hong-Yan Xu
International Journal of Mathematics and Mathematical Sciences , 2007, DOI: 10.1155/2007/84961
Abstract: We deal with some uniqueness theorems of two transcendental meromorphic functions with their nonlinear differential polynomials sharing a small function. These results in this paper improve those given by C.-Y. Fang and M.-L. Fang (2002), by Lahiri and Pal (2006), and by Lin and Yi (2004).
Uniqueness of Meromorphic Functions of Differential Polynomials Sharing Two Values IM  [PDF]
Xinhua Shi
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.42005
Abstract:

In this paper, we shall study the uniqueness problems of meromorphic functions of differential polynomials sharing two values IM. Our results improve or generalize many previous results on value sharing of meromorphic functions.

Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function  [PDF]
Harina P. Waghamore, Tanuja Adaviswamy
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.211191
Abstract: In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function. We consider the case for some general differential polynomials [fnP(f)f,] where P(f) is a polynomial which generalize some result due to Abhijit Banerjee and Sonali Mukherjee [1].
Uniqueness of Meromorphic Functions Whose Differential Polynomials Share One Value  [PDF]
Jin Tao, Xinli Wang
Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.611188
Abstract: In this paper, we prove a uniqueness theorem of meromorphic functions whose some nonlinear differential shares 1 IM with powers of the meromorphic functions, where the degrees of the powers are equal to those of the nonlinear differential polynomials. This result improves the corresponding one given by Zhang and Yang, and other authors.
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