Uniqueness of meromorphic functions sharing two sets having deficient
values

A. Banerjee; S. Mallick

With the aid of weighted sharing of sets we study the uniqueness problem of meromorphic functions having the same pole sharing of a finite set. The result of the paper improves, generalizes and extends a recent result of S. S. Bhoosnurmath and R. Davanal ([1]).

1. S.S. Bhoosnurmath, R. Davanal, Uniqueness of meromorphic functions sharing sets, Bull. Math. Anal. Appl., 3 (2011), №3, 200–208.

2. M. Fang, H. Guo, On meromorphic functions sharing two values, Analysis, 17 (1997), 355–366.

3. M. Fang, X. Hua, Meromorphic functions that share one finite set CM, J. Nanjing Univ. Math. Biquart., 15 (1998), №1, 15–22.

4. M. Fang, I. Lahiri, Unique range set for certain meromorphic functions, Indian J. Math., 45 (2003), №2, 141–150.

5. F. Gross, Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Kentucky(1976); Lecture Notes in Math., 599 (1977), 51–69, Springer (Berlin).

6. W.K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.

7. I. Lahiri, The range set of meromorphic derivatives, Northeast. Math. J., 14 (1998), №3, 353–360.

8. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28 (2001), №2, 83–91.

9. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206.

10. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables, 46 (2001), 241–253.

11. I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38 (2002), 119–128.

12. I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J., 44 (2004), 575–584.

13. I. Lahiri, S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26 (2003), 95–100.

14. A.Z. Mokhon’ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions. Funct. Anal. Appl., 14 (1971), 83–87. (in Russian)

15. H.X. Yi, A question of Gross and the uniqueness of entire functions, Nagoya Math. J., 138 (1995), 169–177.

16. H.X. Yi, Unicity theorems for meromorphic or entire functions, II, Bull. Austral. Math. Soc., 52 (1995), 215–224.

17. H.X. Yi, W.C. Lin, Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J., 46 (2006), 437–444.

18. H.X. Yi, W.R. Lu, Meromorphic functions that share two sets, II, Acta Math. Sci. Ser. B (Engl. Ed.), 24 (2004), №1, 83–90.

	Uniqueness of meromorphic functions sharing two sets having deficient values
Author	A. Banerjee, S. Mallick abanerjee_kal@yahoo.co.in, abanerjee_kal@rediffmail.com Department of Mathematics, University of Kalyani, West Bengal, India
Abstract	With the aid of weighted sharing of sets we study the uniqueness problem of meromorphic functions having the same pole sharing of a finite set. The result of the paper improves, generalizes and extends a recent result of S. S. Bhoosnurmath and R. Davanal ([1]).
Keywords	meromorphic functions; uniqueness; weighted sharing; shared set
Reference	1. S.S. Bhoosnurmath, R. Davanal, Uniqueness of meromorphic functions sharing sets, Bull. Math. Anal. Appl., 3 (2011), №3, 200–208. 2. M. Fang, H. Guo, On meromorphic functions sharing two values, Analysis, 17 (1997), 355–366. 3. M. Fang, X. Hua, Meromorphic functions that share one finite set CM, J. Nanjing Univ. Math. Biquart., 15 (1998), №1, 15–22. 4. M. Fang, I. Lahiri, Unique range set for certain meromorphic functions, Indian J. Math., 45 (2003), №2, 141–150. 5. F. Gross, Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Kentucky(1976); Lecture Notes in Math., 599 (1977), 51–69, Springer (Berlin). 6. W.K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964. 7. I. Lahiri, The range set of meromorphic derivatives, Northeast. Math. J., 14 (1998), №3, 353–360. 8. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28 (2001), №2, 83–91. 9. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206. 10. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables, 46 (2001), 241–253. 11. I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38 (2002), 119–128. 12. I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J., 44 (2004), 575–584. 13. I. Lahiri, S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26 (2003), 95–100. 14. A.Z. Mokhon’ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions. Funct. Anal. Appl., 14 (1971), 83–87. (in Russian) 15. H.X. Yi, A question of Gross and the uniqueness of entire functions, Nagoya Math. J., 138 (1995), 169–177. 16. H.X. Yi, Unicity theorems for meromorphic or entire functions, II, Bull. Austral. Math. Soc., 52 (1995), 215–224. 17. H.X. Yi, W.C. Lin, Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J., 46 (2006), 437–444. 18. H.X. Yi, W.R. Lu, Meromorphic functions that share two sets, II, Acta Math. Sci. Ser. B (Engl. Ed.), 24 (2004), №1, 83–90.
Pages	168-178
Volume	41
Issue	2
Year	2014
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Uniqueness of meromorphic functions sharing two sets having deficient values