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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.13 no.3 Temuco oct. 2011 

CUBO A Mathematical Journal Vol.13, Nº03, (57–67). October 2011


Some Uniqueness Results On Meromorphic Functions Sharing Three Sets II


Abhijit Banerjee 1

Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), West Bengal, Kolkata-700126, India. email:,


With the help of the notion of weighted sharing we investigate the uniqueness of meromorphic functions concerning three set sharing and significantly improve two results of Zhang [16] and as a corollary of the main result we improve a result of the present author [2] as well.

Keywords. Meromorphic functions, uniqueness, weighted sharing, shared set.


Con la ayuda del concepto de peso repartido, investigamos la unicidad de funciones meromorfas sobre un conjunto compartido y mejoramos significativamente dos resulta- dos de Zhang [16] y como corolario del resultado principal que mejoramos también el resultado de la autora [2].

Mathematics Subject Classification: 30D35.


1The author dedicates the paper to the memory of his respected teacher Late Prof. B. K. Lahiri who first germinated the inquisition for research work in the author’s mind.


[1] A.Banerjee, On a question of Gross, J. Math. Anal. Appl. 327(2) (2007) 1273-1283.

[2] A.Banerjee, Some uniqueness results on meromorphic functions sharing three sets, Ann. Polon. Math., 92(3)(2007), 261-274.         [ Links ]

[3] M.Fang and W. Xu, A note on a problem of Gross, Chinese J. Contemporary Math., 18(4)(1997), 395-402.

[4] F.Gross, Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Ky(1976); Lecture Notes in Math., 599(1977), 51-69, Springer(Berlin).         [ Links ]

[5] W.K.Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).         [ Links ]

[6] I.Lahiri, Value distribution of certain differential polynomials. Int. J. Math. Math. Sci., 28(2)(2001), 83-91.

[7] I.Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206.

[8] I.Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.         [ Links ]

[9] I.Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128.         [ Links ]

[10] I.Lahiri and A.Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyung- pook Math. J., 44(2004), 575-584.

[11] I.Lahiri and A.Banerjee, Weighted sharing of two sets, Kyungpook Math. J., 46(1) (2006), 79-87.         [ Links ]

[12] A.Z.Mohon’ko, On the Nevanlinna characteristics of some meromorphic functions,. Theory of Functions. Functional Analysis and Their Applications, 14 (1971), 83-87.

[13] H.Qiu and M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc., 25(2002) 31-38.

[14] H.X.Yi, Meromorphic functions that share one or two values II, Kodai Math. J., 22 (1999), 264-272.

[15] H.X.Yi andW.C.Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad., 80, Ser.A(2004), 136-140.         [ Links ]

[16] Q. Zhang, Meromorphic Functions That Share Three Sets, Northeast Math. J., 23(2)(2007), 103-114.

Received: January 2010. Revised: August 2010.

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