Uniqueness Theorems Of Meromorphic Functions Research Articles

A uniqueness theorem for meromorphic functions

In this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane $\mathbb{C}$. In particular, we study the class of meromorphic functions $f$ in the domain $\mathbb{C}\setminus K'$, where $K'$ is the finite set of limit points of simple poles of the function $f$. In this class, we describe non-trivial subclasses in which every function $f$ can be uniquely determined by the residues of the function $f$ at its poles. The result covered in this paper is a part of a problem in a spectral operator theory.

Uniqueness Theorems of Meromorphic Functions and Their Differences in Several Complex Variables

In this paper, making use of the value distribution theory for meromorphic functions in several complex variables and its difference analogues, we mainly consider the uniqueness problem for meromorphic functions in several complex variables sharing values or small functions with their shifts or difference operators, and weaken the condition of growth of hyper-order of meromorphic functions, which generalize the corresponding results of one complex variable.

A Uniqueness Theorem for Meromorphic Functions Concerning Total Derivatives in Several Complex Variables

Motivated by many differences for the total derivative between entire functions and meromorphic functions, we mainly investigate the uniqueness problems for meromorphic functions in several complex variables concerning the total derivatives. Let f and g be two nonconstant meromorphic functions on $$\mathbb {C}^{m},$$ k be a positive integer such that $$f=0\Leftrightarrow g = 0, D^{k}f=\infty \Leftrightarrow D^{k}g=\infty , D^{k}f=1\Leftrightarrow D^{k}g=1.$$ We get that if $$2\delta (0, f)+(k+4)\varTheta (\infty , f)>k+5,$$ then $$\frac{D^{k}f-1}{D^{k}g-1}$$ is a nonzero constant. This is an extension of a uniqueness theorem for entire functions due to L. Jin. There are several examples to show that our result is sharp.

On the Uniqueness of Meromorphic Functions on Annuli in terms of Deficiencies

The purpose of this article is to study the uniqueness of meromorphic functions on annuli. Under a certain condition about deficiencies, we prove some new uniqueness theorems of meromorphic functions on the annulus A=z:1/R0<z<R0, where 1<R0≤+∞.

Uniqueness theorems for meromorphic functions on annuli

Uniqueness theorems for meromorphic functions on annuli

On Uniqueness of Meromorphic Functions and Their Difference Operators with Partially Shared Values

In this paper, we prove a uniqueness theorem for meromorphic functions and their difference operators with one CM value and two partially shared values. Consequently, not only we give a simple proof of a conjecture posed by Chen and Yi using a new method which is very different from the one proposed by Lu and Lu, but our result is also more general than the related ones due to Chen and Yi, Zhang and Liao, and Lu and Lu.

Uniqueness of meromorphic functions sharing two finite sets

Abstract We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.

Brück Conjecture and Linear Differential Polynomials

In the paper we prove a uniqueness theorem for meromorphic functions that share a function of slower growth with linear differential polynomials. Our result is closely related to a conjecture of Bruck.

Notes on meromorphic functions sharing small function and its derivatives

In this paper we study the uniqueness theorems of meromorphic functions which share a small function with its derivatives, and give some results which are related to the results of P. Li.

Value distribution of certain difference polynomials of meromorphic functions

In this paper, we establish a theorem concerning value distribution of certain difference polynomials of meromorphic functions, which extends [{\bf14}, Theorem 2] and [{\bf16}, Theorem 1.2]. Applying this result, we prove some uniqueness theorems of meromorphic functions whose certain difference polynomials share a non-zero polynomial, which extends [{\bf18}, Theorems 1.1 and 1.2] and [{\bf23}, Theorem 6], where the meromorphic functions are of finite order.

Uniqueness of Q-Difference Polynomials of Meromorphic Functions

In this paper, Applying the theory of Nevanlinna, we investigated uniqueness problem of difference polynomial of meromorphic functions and obtained uniqueness theorems of meromorphic functions , which Extended and improved the results of literature [5].

Meromorphic functions that share one small function DM with their first derivative

In [1] we proved some uniqueness theorems for meromorphic functions that share one nonzero finite value DM (different multiplicities) with their first derivative. In this paper we shall prove that the theorems in [1] are also true if the “value” DM is replaced by “small function” DM.

Uniqueness and Value Sharing of Meromorphic Functions With Regard to Multiplicity

In this paper,we study the uniqueness theorems of meromorphic functions,concerning differential polynomials and obtain theorems, from which we obtain as a very special case the results of Lin and Yi cite[4],Xiao Yu Zhang,Jun-Fan Chen,Wei-Chuan lin[8],and Renukadevi S. Dyavanal[9]. We also obtain several new interesting results.

Meromorphic functions that share a nonzero polynomial IM

We study the uniqueness theorems of meromorphic functions concerning differential polynomials sharing a nonzero polynomial IM, and obtain two theorems which will supplement two recent results due to X. M. Li and L. Gao.

On a Result of N. Terglane

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, which improves a result given by N. Terglane in 1989 and a result given by X. M. Li and H. X. Yi in 2003. Some examples are provided to show that the result of the paper is best possible.

Uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a polynomial

In this paper, we get two uniqueness theorems of meromorphic functions whose certain nonlinear differential polynomials share a polynomial. The results in this paper extend the corresponding results given by Fang (2002) in [7]. Our reasoning in this paper will correct a defective reasoning in the proof of Theorem 4 in Bhoosnurmath and Dyavanal (2007) [8]. An example is provided to show that some conditions of the main results in this paper are necessary.

Uniqueness theorems of meromorphic functions sharing three values

In this article, we deal with the uniqueness problem of meromorphic functions that share three values CM. The results in this article improve and supplement those given by Yi, Li & Yi and other authors.

Uniqueness theorems for meromorphic functions concerning fixed points

Uniqueness theorems for meromorphic functions concerning fixed points

On Some Uniqueness Theorems of Meromorphic Functions Sharing Three Values

We prove some uniqueness theorems of meromorphic functions sharing three values which improves some results of Banerjee.

ON A UNIQUENESS THEOREM OF H. UEDA

We prove a uniqueness theorem for meromorphic functions sharing three weighted values which improves some existing results.