Multi-dimensional almost periodic type functions and applications

Abstract

In this paper, we analyze multi-dimensional $({\mathrm{R}}_X,\mathcal{B})$-almost periodic type functions and multi-dimensional Bohr $\mathcal{B}$-almost periodic type functions. The main structural characterizations and composition principles for the introduced classes of almost periodic functions are established. Several applications of our abstract theoretical results to the abstract Volterra integro-differential equations in Banach spaces are provided, as well.