Uniqueness Of Meromorphic Functions Research Articles

On the multiple values and uniqueness of meromorphic functions on annuli

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions on annuli. We prove a general theorem on the multiple values and uniqueness of meromorphic functions on annuli, from which an analog of Nevanlinna’s famous five-value theorem is proposed.

Fixed-points and uniqueness of meromorphic functions

In the paper, we study the uniqueness and the shared fixed-points of meromorphic functions and prove two main theorems which improve the results of Fang and Fang and Qiu.

Meromorphic functions in the unit disc that share values in an angular domain

In this paper, we investigate the uniqueness of meromorphic functions in the unit disc and consider the relation between the Borel points and shared-values of meromorphic functions in an angular domain.

On the uniqueness of meromorphic functions that share four values in one angular domain

The main purpose of this paper is to investigate the uniqueness of transcendental meromorphic functions that share four values in one angular domain which is an unbounded subset of the whole complex plane. From one of our main results, a question of J.H. Zheng [J.H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domain, Complex Var. Elliptic Equ. 48 (9) (2003) 777–785] is completely answered. Furthermore, we give an example to explain the necessity of the condition lim r → ∞ S α , β ( r , f ) log ( r T ( r , f ) ) = ∞ in our results.

Uniqueness of Meromorphic Functions That Share Three Sets

In the paper we prove some results related to the uniqueness of meromorphic as well as entire functions. Our results will improve and supplement several known results .

Convexity of a family of meromorphically univalent functions by using two fixed points

In this paper a new class of meromorphic univalent functions in terms of an integral operator F c ( z ) = ∫ 0 1 c v c f ( v z ) d v , ( c ≥ 1 ) , is defined. We find some properties of this new class by using two fixed points.

Hadamard product of certain meromorphic starlike and convex functions

In this paper, the authors establish certain results concerning the Hadamard product for two classes related to starlike and convex univalent meromorphic functions of order α and type β with positive coefficients.

On Uniqueness of Meromorphic Functions with Multiple Values in Some Angular Domains

This article deals with problems of the uniqueness of transcendental meromorphic function with shared values in some angular domains dealing with the multiple values which improve a result of J. Zheng.

On the uniqueness of meromorphic functions that share three sets

With the aid of the notion of weighted sharing and pseudo sharing of sets we prove three uniqueness results on meromorphic functions sharing three sets, all of which will improve a result of Lin-Yi in Complex Var. Theory Appl. (2003).

Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight

Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight

Uniqueness for meromorphic functions and differential polynomials

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, \alpha be a meromorphic function such that T(r,\alpha)=o(T(r,f)+T(r,g)) and \alpha \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If \Psi_f' and \Psi_g' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi_1,\varpi_2)=(n+1)(\varpi_1^{n+2}-\varpi_2^{n+2})-(n+2)(\varpi_1^{n+1} -\varpi_2^{n+1}). The results in this paper improve the results of Xiong-Lin-Mori 14 and the author 12.

Meromorphic Functions with Three Weighted Sharing Values

In this paper, we prove some results on uniqueness of meromorphic functions with three weighted sharing values. The results in this paper improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary and H. X. Yi and other authors.

Uniqueness for Meromorphic Functions Concerning Differential Polynomials

Abstract Using the notion of weighted sharing of values which was introduced by I. Lahiri [Nagoya Math. J. 161: 193–206, 2001], we deal with the uniqueness problem of meromorphic functions concerning differential polynomials and obtain some theorems which not only improve a recent result of W. L. Xiong, W. C. Lin and S. Mori [Sci. Math. Jpn. 62: 305–315, 2005], but also improve and supplement the result of W. C. Lin and H. X. Yi [Complex Var. Theory Appl. 49: 793–806, 2004].

Uniqueness of meromorphic functions and differential polynomials

In this paper, we study the uniqueness theorem of meromorphic functions concerning differential polynomials, and obtain two theorems, which improve and generalize the related results of Fang, S.S. Bhoosnurmath and R.S. Dyavanal and Xiao-Yu Zhang and Wei-Chuan Lin.

Uniqueness of meromorphic functions whose derivatives share four small functions

In this paper, we will prove some uniqueness theorems of meromorphic functions whose derivatives share four distinct small functions. The results in this paper improve those given by R. Nevanlinna, L. Yang, G.D. Qiu, and other authors. An example is provided to show that the results in this paper are best possible.

Weighted sharing of meromorphic functions relative to small functions

Using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions with three weighted sharing values. The results in this paper improve those given by H.X. Yi, T.C. Alzahary and H.X. Yi, T.C. Alzahary, I. Lahiri and N. Mandal, and other authors.

Generalizations of Hadamard products of certain meromorphic univalent functions with positive coefficients

AbstractThe authors establish certain results concerning the generalized Hadamard products of certain meromorphic univalent functions with positive coefficients analagous to the results due to Choi et al. (J. Math. Anal. Appl. 199(1996), 495–501).

On uniqueness of meromorphic functions sharing three sets

Using the notion of weighted sharing of sets we deal with the problem of uniqueness of meromorphic functions sharing three sets and obtain three results two of which will improve and the other will supplement a result of Lin-Yi [12].

ON THE MULTIPLE VALUES AND UNIQUENESS OF MEROMORPHIC FUNCTIONS SHARING SMALL FUNCTIONS AS TARGETS

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions with small functions in the whole complex plane. We obtain a more general theorem which improves and extends strongly the results of R. Nevanlinna, Li-Qiao, Yao, Yi, and Thai-Tan.

Small functions and uniqueness of meromorphic functions

We discuss the uniqueness of meromorphic functions sharing three weighted values and provide a complete answer to a question of T.C. Alzahary.