Abstract:In the paper we discuss the uniqueness of the $n$-th power of a meromorphic function sharing a small function with the power of its $k$-th derivative and improve and supplement a result of Zhang-L\"u [Complex Var.\ Elliptic Equ.\ {\bf 53} (2008), no.~9, 857--867]. We also rectify one recent result obtained by Chen and Zhang in [Kyungpook Math.~J.\ {\bf 50} (2010), no.~1, 71--80] dealing with a question posed by T.D.~Zhang and W.R.~L\"u in [Complex Var.\ Elliptic Equ.\ {\bf 53} (2008), no.~9, 857--867].
Keywords: meromorphic function, derivative, small function, weighted sharing
AMS Subject Classification: 30D35