  A sequence $(x_{n})$ of points in a topological group is called
$\Delta$-quasi-slowly oscillating if $(\Delta x_{n})$ is quasi-slowly
oscillating, and is called quasi-slowly oscillating if $(\Delta x_{n})$ is
slowly oscillating. A function $f$ defined on a subset of a topological group
is quasi-slowly (respectively, $\Delta$-quasi-slowly) oscillating continuous if
it preserves quasi-slowly (respectively, $\Delta$-quasi-slowly) oscillating
sequences, i.e. $(f(x_{n}))$ is quasi-slowly (respectively,
$\Delta$-quasi-slowly) oscillating whenever $(x_{n})$ is. We study these kinds
of continuities, and investigate relations with statistical continuity,
lacunary statistical continuity, and some other types of continuities in
metrizable topological groups.
