# UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS OF A CERTAIN FORM

• Xu, Junfeng (Department of Mathematics Wuyi University) ;
• Han, Qi (Department of Mathematics University of Houston) ;
• Zhang, Jilong (LMIB and Department of Mathematics Beihang University)
• 발행 : 2009.11.30

#### 초록

In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

#### 참고문헌

1. J. Clunie, On integral and meromorphic functions, J. London Math. Soc. 37 (1962), 17-27 https://doi.org/10.1112/jlms/s1-37.1.17
2. J. Clunie, On a result of Hayman, J. London Math. Soc. 42 (1967), 389-392 https://doi.org/10.1112/jlms/s1-42.1.389
3. M. L. Fang and W. Hong, A unicity theorem for entire functions concerning differential polynomials, Indian J. Pure Appl. Math. 32 (2001), no. 9, 1343-1348
4. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964
5. W. K. Hayman, Research Problems in Function Theory, The Athlone Press University of London, London 1967
6. W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9-42 https://doi.org/10.2307/1969890
7. P. C. Hu, P. Li, and C. C. Yang, Unicity of Meromorphic Mappings, Advances in Complex Analysis and its Applications, 1. Kluwer Academic Publishers, Dordrecht, 2003
8. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math. 35 (2004), no. 2, 121-132
9. C. C. Yang, On deficiencies of differential polynomials. II, Math. Z. 125 (1972), 107-112 https://doi.org/10.1007/BF01110921
10. C. C. Yang and X. H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), no. 2, 395-406
11. C. C. Yang and X. H. Hua, Unique polynomials of entire and meromorphic functions, Mat. Fiz. Anal. Geom. 4 (1997), no. 3, 391-398
12. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003
13. H. X. Yi, Meromorphic functions that share one or two values, Complex Variables Theory Appl. 28 (1995), no. 1, 1-11 https://doi.org/10.1080/17476939508814833

#### 피인용 문헌

1. Uniqueness Theorems of Difference Operator on Entire Functions vol.2013, 2013, https://doi.org/10.1155/2013/361491
2. Uniqueness Theorems on Difference Monomials of Entire Functions vol.2012, 2012, https://doi.org/10.1155/2012/407351