Uniqueness Of Meromorphic Functions Research Articles

RETRACTED: Uniqueness of meromorphic functions and differential polynomials sharing one value IM

This article has been retracted at the request of the Editors-in-Chief. Please see Elsevier Policy on Article Withdrawal ( http://www.elsevier.com/locate/withdrawalpolicy ). Reason: The editors regret that there is continued uncertainty concerning the status of Theorems 1 and 2 of this article. Consequently, the editors have decided to retract this article. We apologize to all concerned for this necessary course of action.

Weighted sharing of a small function by a meromorphic function and its derivative

The paper deals with the problem of meromorphic functions sharing a small function with its derivative and improves the results of Yu [K.W. Yu, On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4 (1) (2003) Art. 21 (Online: http://jipam.vu.edu.au/)], Lahiri–Sarkar [I. Lahiri, A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5 (1) (2004) Art. 20 (Online: http://jipam.vu.edu.au/)] and a recent result of Zhang [Q.C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (4) (2005) Art. 116 (Online: http://jipam.vu.edu.au/)].

Meromorphic functions sharing three values with finite weight

Using the idea of weighted sharing we prove some theorems on uniqueness of meromorphic functions that share three values, which improve and supplement some results of Yi. Also we solve a problem recently raised by the present author [Austral. J. Math. Anal. Appl. 3 (2006)]. Examples are provided to show that some results are sharp.

On a question of Gross

Using the notion of weighted sharing of sets we prove two uniqueness theorems which improve the results proved by Fang and Qiu [H. Qiu, M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc. 25 (2002) 31–38], Lahiri and Banerjee [I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004) 575–584] and Yi and Lin [H.X. Yi, W.C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80 (2004) 136–140] and thus provide an answer to the question of Gross [F. Gross, Factorization of meromorphic functions and some open problems, in: Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, in: Lecture Notes in Math., vol. 599, Springer, Berlin, 1977, pp. 51–69], under a weaker hypothesis.

Uniqueness of meromorphic functions concerning weakly weighted-sharing

In this paper, we introduce the definition of weakly weighted-sharing which is between CM and IM. Using the notion of weakly weighted-sharing, we study the uniqueness problems on meromorphic function and its kth order derivative f(k) satisfying certain sharing set properties. As consequences, we are able to answer questions posed by Kit-wing Yu, which were also studied by I. Lahiri and A. Sarkar, L. P. Liu and Y. X. Gu. Our results sharpen the above results.

Uniqueness of meromorphic functions and a question of K. Tohge

We prove a uniqueness theorem for meromorphic functions sharing three values, which answers a question asked by K. Tohge.

Notes on Uniqueness of Meromorphic Functions

In this paper, we study the problem of uniqueness on meromorphic functions involving in differential polynomials and obtain some results which extend and improve the theorems of M. Fang and W. Hong et al.

Small functions and weighted sharing three values

This article studies the problem of the uniqueness of meromorphic functions that weighted sharing three values which improve some results given by Yi [Theorem 4, Yi, H.X., 1995, Unicity theorems for meromorphic functions that share three values. Kodai Mathematical Journal, 18, 300-314] and Ueda [Ueda, H., 1983, Unicity theorems for meromorphic or entire functions II. Kodai Mathematical Journal, 6, 26-36] and other authors. An application of these new results, if f and g are two distinct nonconstant meromorphic functions sharing 0, 1 and CM, and a is a nonconstant rational function, then N2)(r,1/(g-a))= [image omitted] An example shows that the latter result is not true for some transcendental small functions of f and g.

Meromorphic functions with weighted sharing of three values

In this article we study the problem of uniqueness of meromorphic functions with weighted sharing of three values. The results in this article improve some theorems of M. Ozawa, H. Ueda, G. Brosch, H. Yi, I. Lahiri and other authors. Examples are provided to show that the conditions of our results are sharp.

On the results of Lahiri concerning uniqueness of meromorphic functions

In this paper we study the problem of meromorphic functions sharing three values with weight and obtain some theorems which improve the results given by Lahiri and others.

On Gundersen’s question for the unicity of meromorphic functions

The uniqueness of meromorphic functions that share four values are investigated, some results are obtained to show that if two nonconstant entire functions share three finite values IM, then the functions necessarily share all three values CM.

Neighborhoods and Partial Sums of Meromorphic Univalent Functions

In this paper we determine neighborhood results and partial sums for certain class of meromorphic univalent functions with positive coefficients defined by Ruscheweyh derivatives. 2000 Mathematica Subject Classification: 30C45.

Weighted value sharing and a question of I. Lahiri

In this article, we investigate the problem due to I. Lahiri [I. Lahiri (2001). Weighted value sharing and uniqueness of meromorphic functions. Complex Variables Theory Appl., 46, 241–253.]. Also we prove some uniqueness theorems of meromorphic functions which improve some earlier results.

MEROMORPHIC FUNCTIONS THAT SHARE FOUR VALUES

The uniqueness of meromorphic functions that share four values is investigated. A necessary condition to the case is acquired, and some partial results for question “1CM+3IM=4CM” are obtained.

Weighted sharing three values and uniqueness of meromorphic functions

Using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions sharing three values which improve some results given by H.-X. Yi, I. Lahiri, X. Hua and other authors.

Poles near the origin produce lower bounds for coefficients of meromorphic univalent functions

Poles near the origin produce lower bounds for coefficients of meromorphic univalent functions

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

AbstractIn this paper we investigate the uniqueness of transcendental meromorphic function dealing with the shared values in some angular domains instead of the whole complex plane.

Uniqueness Theorems for Meromorphic Functions That Share Three Sets

In this article, we deal with the problem of uniqueness of meromorphic functions that share three sets, and obtain one set S with 5 elements such that any two nonconstant meromorphic functions ƒ and g satisfying E(S, ƒ) = E(S, g), E({0}, ƒ) = E({0}, g) and E({∞}, ƒ) = E({∞}, g) must be identical.

On Uniqueness of Meromorphic Functions with Shared Values in One Angular Domain

In this article we investigate the uniqueness of transcendental meromorphic function dealing with four shared values in one angular domain instead of the whole complex plane.

On a result of Ozawa concerning uniqueness of meromorphic functions

In this paper we prove a uniqueness theorem for meromorphic functions sharing three values with some weight which improves some known results.