Abstract
G. Jank, E. Mues and L. Volkmann proved that if a nonconstant meromorphic function f shares a nonzero finite value a CM (counting multiplicities) with its first two derivatives f′ and , then f≡f′. It is also noted there that this is not the case for a=0. In this note we consider the case a=0 and IM (ignoring multiplicities) under certain andiiional conditions, one of which requires that the third order derivative should also share 0 IM with and the other is on the number of the zeros and multiple poles of f. We prove that each of the conditions can reduce f/f′ to possibly a linear polynomial
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