MEROMORPHIC FUNCTIONS SHARING A NONZERO POLYNOMIAL CM

In this paper, we prove that if f(n) f' - P and g(n) g' - P share 0 CM, where f and g are two distinct transcendental meromorphic functions, n >= 11 is a positive integer, and P is a nonzero polynomial such that its degree gamma p <= 11, then either f = c(1)e(cQ) and g = c(2)e(-cQ), where c(1), c(2) and c are three nonzero complex numbers satisfying (c(1)c(2))(n+1) c(2) = -1, Q is a polynomial such that Q = integral(z)(0) P(eta)d eta, or f = tg for a complex number t such that t(n+1) = 1. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Him., and other authors.