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: abanerjee_kal@yahoo.co.in, abanerjee_kal@rediffmail.com

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ABSTRACT

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.

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RESUMEN

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.

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Notas

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.

References

[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.

[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).

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

[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.

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

[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.

[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.

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

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Received: January 2010. Revised: August 2010.