SOME RESULTS ON VALUE DISTRIBUTION OF THE DIFFERENCE OPERATOR

In this article, we consider the uniqueness of the difference monomials f(n)(z) f(z + c). Suppose that f(z) and g(z) are transcendental meromorphic functions with finite order and E-k(1, f(n)(z) f(z + c)) = E-k(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) equivalent to t(1g)(z) or f(z)g(z) = t(2), for some constants t(1) and t(2) that satisfy t(1)(n+1) = 1 and t(2)(n+1) = 1. We generalize some previous results of Qi et. al.