ON THE UNIQUENESS OF ENTIRE FUNCTIONS

Title & Authors
ON THE UNIQUENESS OF ENTIRE FUNCTIONS
Qiu, Huiling; Fang, Mingliang;

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, $\small{n\;{\geq}\;7}$ a positive integer, and let a be a nonzero finite complex number. If $\small{f^{n}(z)(f(z)\;-\;1)f(z)\;and\;g^{n}(z)(g(z)\;-\;1)g(z)}$ share a CM, then $\small{f(z)\;{\equiv}\;g(z)}$. The result improves the theorem due to ref. [3].
Keywords
entire function;sharing value;uniqueness;
Language
English
Cited by
1.
UNIQUENESS OF ENTIRE FUNCTIONS AND DIFFERENTIAL POLYNOMIALS,;;

대한수학회보, 2007. vol.44. 4, pp.623-629
2.
Uniqueness of Certain Non-Linear Differential Polynomials Sharing 1-Points,;

Kyungpook mathematical journal, 2011. vol.51. 1, pp.43-58
1.
A uniqueness result related to certain non-linear differential polynomials sharing the same 1-points, Mathematica Slovaca, 2011, 61, 2
2.
Uniqueness of Certain Non-Linear Differential Polynomials Sharing 1-Points, Kyungpook mathematical journal, 2011, 51, 1, 43
3.
Generalization of Uniqueness Theorems for Entire and Meromorphic Functions, Applied Mathematics, 2014, 05, 08, 1267
4.
Value Distributions and Uniqueness of Difference Polynomials, Advances in Difference Equations, 2011, 2011, 1
References
1.
Meromorphic functions,

2.
Value distribution theory,

3.
Indian J. of Pure and Appl. Math., vol.32. 9, pp.1343-1348

4.
Math. Z., vol.125. pp.107-112

5.
Unicity theory of meromorphic functions,

6.
Le thoreme de Picard-Borel et la theorie des fonctions meromorphes,

7.
J. of Nanjing Univ. Mathematical Biquarterly, vol.13. 1, pp.44-48

8.
Ann. Acad. Sci. Fenn. Math., vol.22. 2, pp.395-406

9.
Tokohama Math. J., vol.44. 2, pp.147-156

10.
Complex Variables, vol.39. pp.85-92