Multi-dimensional $c$-almost periodic type functions and applications

TL;DR

This paper studies multi-dimensional Bohr $({\mathcal B},c)$-almost periodic functions, providing structural characterizations and applying these results to abstract Volterra integro-differential equations in Banach spaces.

Contribution

It introduces new classes of multi-dimensional Bohr $({\mathcal B},c)$-almost periodic functions and establishes their structural properties, with applications to integro-differential equations.

Findings

Structural characterizations of Bohr $({\mathcal B},c)$-almost periodic functions

Application to Volterra integro-differential equations in Banach spaces

Extension of almost periodic function theory to multi-dimensional settings

Abstract

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