A note on meromorphic functions that share a set with their derivatives

In this paper, we study a problem of meromorphic functions that share an arbitrary set having three elements with their derivatives. A uniqueness result is derived which is an improvement of some related theorems given by Fang and Zalcman (J. Math. Anal. Appl. 280 (2003), 273–283) and Chang, Fang, and Zalcman (Arch. Math. 89 (2007), 561–569). As an application, we generalize the famous Brück conjecture with the idea of sharing a set.