Meromorphic Functions That Share Fixed-Points

In this paper, we prove the following result: Let f(z) and g(z) be two nonconstant meromorphic(entire) functions, n ≥ 11(n ≥ 6) a positive integer. If fⁿ(z)f′(z) and gⁿ(z)g′(z) have the same fixed-points, then either f(z) = c₁e^cz2, g(z) = c₂e^− cz2, where c₁, c₂, and c are three constants satisfying 4(c₁c₂)^n + 1c² = −1, or f(z) ≡ tg(z) for a constant t such that t^n + 1 = 1.