Meromorphic Functions That Share Fixed-Points
2002
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.
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