Results on a question of zhang and yang

For a meromorphic function f  , let N(l+1(r,1f) denote the counting function of zeros of f of order l at least. Let f be a nonconstant meromorphic function, such that . Denote F = fn. Suppose that F and F′ share 1 CM. If (1) n   ≥ 3, or N(r,1f)=O(N(3(r,1f)), then, F = F′, and f assumes the formf(z)=ce1nz,where c is a nonzero constant. This main result of this article gives a positive answer to a question raised by Zhang and Yang [1] for the meromorphic functions case in some sense. And a relative result is proved.