Bulletin of the
Korean Mathematical Society BKMS

In 1996, Br\"{u}ck studied the relation between $f$ and $f'$ if an entire function $f$ shares one value $a$ CM with its first derivative $f'$ and posed the famous Br\"{u}ck conjecture. In this work, we generalize the value $a$ in the Br\"{u}ck conjecture to a small function $\alpha$. Meanwhile, we prove that the Br\"{u}ck conjecture holds for a class of meromorphic functions.

Keywords: entire functions, Nevanlinna theory, uniqueness, normal family

MSC numbers: 30D35, 30D45