Metrical almost periodicity and applications

We analyze various classes of multi-dimensional almost periodic type functions in general metrics. The main classes of functions under 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 $(\mathcal B,I’,\rho ,\mathcal P)$-almost periodic functions and $(\mathcal B,I’,\rho ,\mathcal P)$-uniformly recurrent functions. We clarify the main structural properties of those classes and provide some applications to abstract Volterra integro-differential equations.