Metrical almost periodicity and applications

摘要

We analyze various classes of multi-dimensional almost periodic type functions in general metrics. The main classes of functions under consideration are (R, 8, P, L)-multi-almost periodic functions, (RX, 8, P, L)-multi-almost periodic functions, Bohr (8, I ', rho, P)-almost periodic functions and (8, I ', rho, P)-uniformly recurrent functions. We clarify the main structural properties of those classes and provide some applications to abstract Volterra integro-differential equations.