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Displaying similar documents to “Meromorphic Function Sharinga Small Function with its Differential Polynomial”

Uniqueness theorems for meromorphic functions concerning fixed points

Xiu-Qing Lin, Wei-Chuan Lin (2011)

Annales Polonici Mathematici

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This paper is devoted to the study of uniqueness of meromorphic functions sharing only one value or fixed points. We improve some related results due to J. L. Zhang [Comput. Math. Appl. 56 (2008), 3079-3087] and M. L. Fang [Comput. Math. Appl. 44 (2002), 823-831], and we supplement some results given by M. L. Fang and X. H. Hua [J. Nanjing Univ. Math. Biquart. 13 (1996), 44-48] and by C. C. Yang and X. H. Hua [Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406].

On a result of Zhang and Xu concerning their open problem

Sujoy Majumder, Rajib Mandal (2018)

Archivum Mathematicum

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The motivation of this paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial with the help of the idea of normal family. The result of the paper improves and generalizes the recent result due to Zhang and Xu [24]. Our another remarkable aim is to solve an open problem as posed in the last section of [24].

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.

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.

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.

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.

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.

Further investigation “On an open problem of Zhang and Xu”

Sujoy Majumder (2018)

Mathematica Bohemica

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The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The result of the paper improves and generalizes the recent results due to X. B. Zhang and J. F. Xu (2011). We also solve an open problem posed in the last section of X. B. Zhang and J. F. Xu (2011).

On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)

Open Mathematics

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In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.

Exceptional values of meromorphic functions and of their derivatives on annuli

Yuxian Chen, Zhaojun Wu (2012)

Annales Polonici Mathematici

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This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.

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.