Meromorphic Functions That Share Fixed-Points

AbstractIn 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)=c1ecz2,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 tn+1=1