Meromorphic Functions That Share Fixed-Points

Abstract 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 f n ( z ) f ′( z ) and g n ( z ) g ′( z ) have the same fixed-points, then either f ( z ) =  c 1 e cz 2 ,  g ( z ) =  c 2 e −  cz 2 , where c 1 ,  c 2 , and c are three constants satisfying 4( c 1 c 2 ) n  + 1 c 2  = −1, or f ( z ) ≡  tg ( z ) for a constant t such that t n  + 1  = 1.