# ON THE UNIQUENESS OF ENTIRE FUNCTIONS

• Qiu, Huiling (Department of Mathematics, Nanjing Normal University) ;
• Fang, Mingliang (Department of Mathematics, Nanjing Normal University)
• Published : 2004.02.01
• 108 28

#### Abstract

In this paper, we study the uniqueness of entire functions and prove the following result: Let f(z) and g(z) be two nonconstant entire functions, $n\;{\geq}\;7$ a positive integer, and let a be a nonzero finite complex number. If $f^{n}(z)(f(z)\;-\;1)f'(z)\;and\;g^{n}(z)(g(z)\;-\;1)g'(z)$ share a CM, then $f(z)\;{\equiv}\;g(z)$. The result improves the theorem due to ref. [3].

#### Keywords

entire function;sharing value;uniqueness

#### References

1. Meromorphic functions W.K.Hayman
2. Unicity theory of meromorphic functions H.X.Yi;C.C.Yang
3. Le thoreme de Picard-Borel et la theorie des fonctions meromorphes R.Nevanlinna
4. Tokohama Math. J. v.44 no.2 Uniqueness of meromorphic functions as governed by their diferential polynomials I.Lahiri
5. J. of Nanjing Univ. Mathematical Biquarterly v.13 no.1 Entire functions that share one value M.L.Fang;X.H.Hua
6. Ann. Acad. Sci. Fenn. Math. v.22 no.2 Uniqueness and value-sharing of meromorphic functions C.C.Yang;X.H.Hua
7. Indian J. of Pure and Appl. Math. v.32 no.9 A unicity theorem for entire functions, concerning differential polynomials M.L.Fang;W.Hong;
8. Complex Variables v.39 Meromorphic functions sharing a set with 17 elements ignoring multiplicities S.Bartels https://doi.org/10.1080/17476939908815183
9. Value distribution theory L.Yang
10. Math. Z. v.125 On dificiencies of differential polynomials II C.C.Yang https://doi.org/10.1007/BF01110921

#### Cited by

1. A uniqueness result related to certain non-linear differential polynomials sharing the same 1-points vol.61, pp.2, 2011, https://doi.org/10.2478/s12175-011-0004-7
2. Uniqueness of Certain Non-Linear Differential Polynomials Sharing 1-Points vol.51, pp.1, 2011, https://doi.org/10.5666/KMJ.2011.51.1.043
3. Generalization of Uniqueness Theorems for Entire and Meromorphic Functions vol.05, pp.08, 2014, https://doi.org/10.4236/am.2014.58118
4. Value Distributions and Uniqueness of Difference Polynomials vol.2011, 2011, https://doi.org/10.1155/2011/234215