  In this paper, we relate the notions of remote almost periodicity and
quasi-asymptotical almost periodicity; in actual fact, we observe that a
remotely almost periodic function is nothing else but a bounded, uniformly
continuous quasi-asymptotically almost periodic function. We introduce and
analyze several new classes of remotely $c$-almost periodic functions in
${\mathbb R}^{n},$ slowly oscillating functions in ${\mathbb R}^{n},$ and
further analyze the recently introduced class of quasi-asymptotically
$c$-almost periodic functions in ${\mathbb R}^{n}.$ We provide certain
applications of our theoretical results to the abstract Volterra
integro-differential equations and the ordinary differential equations.
