Displaying similar documents to “Linear differential polynomials sharing the same 1-points with weight two”

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...

Generalization of uniqueness and value sharing of meromorphic functions concerning differential polynomials

Harina P. Waghamore, Ramya Maligi (2020)

Communications in Mathematics

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The motivation of this paper is to study the uniqueness problems of meromorphic functions concerning differential polynomials that share a small function. The results of the paper improve and generalize the recent results due to Fengrong Zhang and Linlin Wu [13]. We also solve an open problem as posed in the last section of [13].

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.

Meromorphic Function Sharinga Small Function with its Differential Polynomial

Abhijit Banerjee, Molla Basir AHAMED (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we improve, generalize and extend a number of recent results related to a problem of meromorphic function sharing a small function with its differential polynomial which are the continuation of a result earlier obtained by R. Brück.

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.

On uniqueness for nonlinear differential polynomials sharing the same 1-point

Abhijit Banerjee (2006)

Annales Polonici Mathematici

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We study the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share the same 1-points. Our results improve results of Fang-Fang and Lin-Yi and supplement a recent result of Lahiri-Pal.

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.

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 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].

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.