Displaying similar documents to “Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight”

Meromorphic functions sharing three values with finite weight

Abhijit Banerjee (2007)

Annales Polonici Mathematici

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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.

Some uniqueness results on meromorphic functions sharing three sets

Abhijit Banerjee (2007)

Annales Polonici Mathematici

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We discuss the uniqueness of meromorphic functions when they share three sets with the notion of weighted sharing and improve two results of Lahiri-Banerjee and Yi-Lin. We also improve a recent result of the present author and thus provide an answer to a question of Gross, in a new direction.

Uniqueness and weighted sharing of meromorphic functions

Pulak Sahoo (2011)

Annales Polonici Mathematici

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We study the uniqueness of meromorphic functions using nonlinear differential polynomials and the weighted value sharing method. Though the main concern of the paper is to improve a recent result of L. Liu [Comput. Math. Appl. 56 (2008), 3236-3245], as a consequence of the main result we also improve and generalize some former results of T. Zhang and W. Lu [Comput. Math. Appl. 55 (2008), 2981-2992], A. Banerjee [Int. J. Pure Appl. Math. 48 (2008), 41-56] and a recent result of the present...

Uniqueness and two shared set problems of meromorphic functions in a different angle

Sanjay Mallick, Abhijit Banerjee (2021)

Mathematica Bohemica

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The purpose of the paper is to represent the two shared set problems in an elaborative and convenient manner. In the main result of the paper, we have exhaustively treated the two shared set problem on the open complex plane. As a consequence of the main result, we have investigated the same problem in a different perspective, which has yet not been studied. Further, two examples have been exhibited in the paper to show the sharpness of some of these results.

Uniqueness of meromorphic functions sharing three values

Indrajit Lahiri, Arindam Sarkar (2005)

Annales Polonici Mathematici

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We prove a result on the uniqueness of meromorphic functions sharing three values with weights and as a consequence of this result we improve a recent result of W. R. Lü and H. X. Yi.

Results on weighted sharing of values for meromorphic functions

Xiao-Min Li, Hong-Xun Yi (2007)

Annales Polonici Mathematici

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We prove some results on uniqueness of functions with three shared values. Our results improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary & H. X. Yi, and other authors.

Investigations on unique range sets of meromorphic functions in an angular domain

Sayantan Maity, Abhijit Banerjee (2023)

Mathematica Bohemica

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We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.

Uniqueness of meromorphic functions sharing two finite sets

Jun-Fan Chen (2017)

Open Mathematics

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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.

Unicity theorems for meromorphic functions that share three values

Wei-Ran Lü, Hong-Xun Yi (2003)

Annales Polonici Mathematici

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We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.

On a question of Hong Xun Yi

Indrajit Lahiri (2002)

Archivum Mathematicum

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In the paper we prove a uniqueness theorem for meromorphic functions which provides an answer to a question of H. X. Yi.

Uniqueness of meromorphic functions sharing a meromorphic function of a smaller order with their derivatives

Xiao-Min Li, Hong-Xun Yi (2010)

Annales Polonici Mathematici

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We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.