SOME RESULTS ON VALUE DISTRIBUTION OF THE DIFFERENCE OPERATOR

In this article, we consider the uniqueness of the difference monomials fn(z)f(z + c). Suppose that f(z) and g(z) are transcendental meromorphic functions with finite order and Ek(1, f n(z)f(z + c)) = Ek(1, g n(z)g(z+ c)). Then we prove that if one of the following holds (i) n ≥ 14 and k ≥ 3, (ii) n ≥ 16 and k = 2, (iii) n ≥ 22 and k = 1, then f(z) ≡ t1g(z) or f(z)g(z) = t2, for some constants t1 and t2 that satisfy t 1 = 1 and t n+1 2 = 1. We generalize some previous results of Qi et. al.

[1]  Lian-Zhong Yang,et al.  PROPERTIES OF MEROMORPHIC SOLUTIONS OF q-DIFFERENCE EQUATIONS , 2015 .

[2]  H. Yi,et al.  On Sharing Values of Meromorphic Functions and Their Differences , 2013 .

[3]  T. Cao.  ENTIRE SOLUTIONS OF FERMAT TYPE q-DIFFERENCE DIFFERENTIAL EQUATIONS , 2013 .

[4]  Kai Liu,et al.  SOME DIFFERENCE RESULTS ON HAYMAN CONJECTURE AND UNIQUENESS , 2012 .

[5]  Xiao-Min Li,et al.  Notes on entire functions sharing an entire function of a smaller order with their difference operators , 2012 .

[6]  Kai Liu,et al.  Entire solutions of Fermat type differential-difference equations , 2012 .

[7]  Jin-Dong Li,et al.  Uniqueness of Meromorphic Functions and Differential Polynomials , 2011, Int. J. Math. Math. Sci..

[8]  Xiao-Min Li,et al.  Uniqueness theorems of entire functions sharing a nonzero complex number with their difference operators , 2011 .

[9]  Wei-Chuan Lin,et al.  Value sharing results for shifts of meromorphic functions , 2011 .

[10]  Kai Liu,et al.  Uniqueness and periodicity of meromorphic functions concerning the difference operator , 2010, Comput. Math. Appl..

[11]  J. Heittokangas,et al.  Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity , 2009 .

[12]  Jilong Zhang,et al.  Non-existence of meromorphic solutions of a Fermat type functional equation , 2008 .

[13]  Y. Chiang,et al.  On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane , 2006, math/0609324.

[14]  R. Korhonen,et al.  Nevanlinna theory for the difference operator , 2005, math/0506011.

[15]  R. Korhonen,et al.  Finite‐order meromorphic solutions and the discrete Painlevé equations , 2005, nlin/0504026.

[16]  R. Korhonen,et al.  Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations , 2005, math/0504245.

[17]  N. Yanagihara,et al.  Wiman-Valiron method for difference equations , 2004, Nagoya Mathematical Journal.

[18]  Ping Li,et al.  Uniqueness of meromorphic functions on ℂ , 2003 .

[19]  F. Gross.  On the distribution of values of meromorphic functions , 1968 .

[20]  W. K. Hayman,et al.  On the characteristic of functions meromorphic in the unit disk and of their integrals , 1964 .