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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

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

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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