SOME RESULTS ON VALUE DISTRIBUTION OF THE DIFFERENCE OPERATOR

ABSTRACT. In this article, we consider the uniqueness of the difference monomials fr(z)f(z + c). Suppose that f(z) and g(z) are transcendental meromorphic functions with finite order and Ek(1, fr(z)f(z + c)) = Ek(1,9"(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) Et19(z) or f(z)g(z) = t2, for some constants t1 and to that satisfy t +1 = 1 and t+1 = 1. We generalize some previous results of Qi et. al.