Abstract:
We investigate various classes of multi-dimensional (S,D,B)-asymptotically
(ω,ρ)-periodic type functions,
multi-dimensional quasi-asymptotically ρ-almost periodic type functions and multi-dimensional ρ-slowly oscillating type functions of the form F:I×X→Y, where
n∈N,∅≠I⊆Rn,ω∈Rn∖{0},X and Y are complex Banach spaces and ρ is a binary relation on Y.
The main structural properties
of these classes of almost periodic type functions
are deduced.
We also provide certain applications of our results to
the abstract Volterra integro-differential equations.
Keywords:(S,D,B)-asymptotically
(ω,ρ)-periodic type functions, quasi-asymptotically ρ-almost periodic type functions, remotely ρ-almost periodic type functions, ρ-slowly oscillating type functions,
abstract Volterra integro-differential equations.