Abstract In this paper we find out the specific form of a
meromorphic function when a generalized linear expression of the
function share a small function with its $k$-th derivative
counterpart. Our result will improve and generalize a few existing
results, especially that of Zhang and Yang [J. L. Zhang and L. Z.
Yang, A power of a meromorphic function sharing a small function
with its derivative, Ann. Acad. Sci. Fenn. Math., 34 (2009),
249-260].
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