Metrical almost periodicity and applications

Abstract

In this paper, we analyze various classes of multi-dimensional almost periodic type functions in general metric. The main classes of functions under our consideration are $(\mathrm{R},\mathcal{B},\mathcal{P},L)$-multi-almost periodic functions, $({\mathrm{R}}_X,\mathcal{B},\mathcal{P},L)$-multi-almost periodic functions, Bohr $(\mathcal{B},I^{\prime },\rho ,\mathcal{P})$-almost periodic functions and $(\mathcal{B},I^{\prime },\rho ,\mathcal{P})$-uniformly recurrent functions. We clarify the main structural properties for the introduced classes of almost periodic type functions and provide some applications of our results to the abstract Volterra integro-differential equations.