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 A note on the Br\"{u}ck conjecture Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 951-957 https://doi.org/10.4134/BKMS.2011.48.5.951Printed September 1, 2011 Feng L\"{u} China University of Petroleum Abstract : 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 Downloads: Full-text PDF