A result on a question of Lü, Li and Yang

Abstract

Let f be a transcendental meromorphic function of finite order with finitely many poles, c ? C\{0} and n,k ? N. Suppose fn(z)-Q1(z) and (fn(z+c))(k)- Q2(z) share (0,1) and f(z), f(z+c) share 0 CM. If n ? k + 1, then (fn(z+c))(k) ? Q2(z)/Q1(z)fn(z), where Q1, Q2 are polynomials with Q1Q2 ?/ 0. Furthermore, if Q1 = Q2, then f(z)=c1e?/n z, where c1 and ? are non-zero constants such that e?c = 1 and ?k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.