JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE DIFFERENTIAL POLYNOMIALS SHARE SOME VALUES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE DIFFERENTIAL POLYNOMIALS SHARE SOME VALUES
MENG, CHAO; LI, XU;
 
 Abstract
In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If fn(f3 - 1)f′ and gn(g3 - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).
 Keywords
Uniqueness;meromorphic function;differential polynomials;
 Language
English
 Cited by
 References
1.
A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions whose n-th derivative share one or two values, Novi Sad J. Math. 39 (2009), 7-19.

2.
C.Y. Fang and M.L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl. 44 (2002), 607-617. crossref(new window)

3.
M.L. Fang and W. Hong, A unicity theorem for entire functions concerning differential polynimials, Indian J. Pure Appl. Math. 32 (2001), 1343-1348.

4.
W.K. Hayman, Meromorphic Functions, Clarendon, Oxford, 1964.

5.
I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206. crossref(new window)

6.
I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), 241-253. crossref(new window)

7.
I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43 (2006), 161-168. crossref(new window)

8.
W.C. Lin and H.X. Yi, Uniqueness theorems for meromorphic functions concerning fixedpoints, Complex Variables Theory and Appl. 49 (2004), 793-806. crossref(new window)

9.
W.C. Lin and H.X. Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math. 35 (2004), 121-132.

10.
C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48 (2008), 25-35. crossref(new window)

11.
C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math. J. 39 (2009), 163-179.

12.
C.C. Yang, On deficiencies of differential polynomials, Math. Z. 125 (1972), 107-112. crossref(new window)

13.
C.C. Yang and X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406.

14.
L. Yang, Value Distribution Theory, Springer-Verlag, Berlin, 1993.

15.
H.X. Yi, Meromorphic functions that share one or two values, Complex Variables Theory Appl. 28 (1995), 1-11. crossref(new window)

16.
H.X. Yi, Uniqueness of meromorphic functions and a question of C.C.Yang, Complex Variables Theory Appl. 14 (1990), 169-176. crossref(new window)

17.
H.X. Yi and L.Z. Yang, Meromorphic functions that share two sets, Kodai Math. J. 20 (1997), 127-134. crossref(new window)

18.
J.L. Zhang, Meromorphic functions sharing a small function with their differential polynomials, Kyungpook Math. J. 50 (2010), 345-355. crossref(new window)