UNIQUENESS OF MEROMORPHIC FUNCTIONS SHARING TWO FINITE SETS IN C

Year 2014, Volume: 2 Issue: 2, 42 - 52, 01.12.2014

ABHIJIT Banerjee GOUTAMHALDAR

Abstract

With the aid of the notion of weighted sharing of sets of meromorphic functions we improve some previous results concerning a particularrange set

Keywords

eromorphic function , Uniqueness , Shared Set , Weighted sharing

References

• A. Banerjee, On the uniqueness of meromorphic functions that share two sets, Georgian Math., Vol:15, No.1 (2008), 21-38. A. Banerjee,
• Uniqueness of meromorphic functions sharing two sets with finite weight, Portugal. Math. (N.S.), Vol:65, No.1 (2008), 81-93.
• A. Banerjee, Some further results ona question of Yi, Publ. De Inst. Math., Vol:92, No.6 (2012), 177-187.
• A. Banerjee, and S. Mukherjee, Uniqueness of meromorphic functions sharing two or three sets, Hokkaido Math. J., Vol:37, No.3 (2008), 507-530.
• A. Banerjee and P. Bhattacharajee, Uniqueness and set sharing of derivatives of meromor- phic functions, Math. Slovaca, Vol:61, No.2 (2011), pp. 197-214.
• M. Fang and H.Guo, On meromorphic functions sharing two values, Analysis, Vol:17 (1997), 355-3
• M. Fang and I. Lahiri, Unique range set for certain meromorphic functions, Indian J. Math., Vol:45, No.2 (2003), 141-150. 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).
• F. Gross and C. C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad., Vol:58 (1982), 17-20.
• W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
• I. Lahiri, The range set of meromorphic derivatives, Northeast. Math. J., Vol:14, No.3 (1998), 353-3
• I. Lahiri,Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., Vol:28, No.2 (2001), 83-91.
• I. Lahiri,Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., Vol:161 (2001), 193-206.
• I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., Vol:46 (2001), 241-253.
• I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), Vol:38 (2002), 119-128. P. Li and C. C. Yang,
• Some further results on the unique range sets for meromorphic functions, Kodai Math. J.,Vol:18 (1995), 437-450.
• P. Li and C. C. Yang, On the unique range sets for meromorphic functions, Proc. Amer. Math. Soc., Vol:124 (1996) 177-185.
• W. C. Lin and H. X. Yi, Some further results on meromorphic functions that share two sets, Kyungpook Math. J., Vol:43 (2003), 73-85.
• A. Z. Mohon’ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions. Funct. Anal. Appl., Vol:14 (1971), 83-87.
• H. X. Yi,Unicity theorems for meromorphic or entire functions II, Bull. Austral. Math. Soc., Vol:52 (1995), 215-224.
• H. X. Yi, Unicity theorems for meromorphic or entire functions III, Bull. Austral. Math. Soc.,Vol:53 (1996), 71-82.
• H. X. Yi and W. C. Lin,Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J, Vol:46 (2006), 437-444.
• H. X. Yi and W. R. L¨u, Meromorphic functions that share two sets II, Acta Math. Sci. Ser.B Engl. Ed., Vol:24 No. 1 (2004), 83-90.
• Department of Mathematics, University of Kalyani, West Bengal 741235, India.
• E-mail address: abanerjee [e-mail], [e-mail]