  In this short note, further to Ng's study, we extend Bekka amenability and
weak Bekka amenability to general locally compact quantum groups. We generalize
some Ng's results to the general case. In particular, we show that, a locally
compact quantum group $\mathbb{G}$ is co-amenable if and only if the
contra-corepresentation of its fundamental multiplicative unitary
$W_{\mathbb{G}}$ is Bekka amenable, and $\mathbb{G}$ is amenable if and only if
its dual quantum group's fundamental multiplicative unitary
$W_{\widehat{\mathbb{G}}}$ is weakly Bekka amenable.
