In this paper, we analyze various classes of multi-dimensional ρ-almost periodic type functions F:I×X→Y and multi-dimensional (ω,ρ)-almost periodic type functions F:I×X→Y,
Nearby in the stack
where
n∈N,
∅=I⊆Rn,
X
and
Y
are complex Banach spaces and
ρ
is a binary relation on
Y.
The proposed notion is new even in the one-dimensional setting, for the functions of the form
F:I→Y.
The main structural properties and characterizations for the introduced classes of functions are presented. We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations, as well.