Multi-dimensional <i>ρ</i> -almost periodic type functions and applications

Abstract

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, 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.