Metrical almost periodicity and applications

2021/11/25 by Kostic, Marko
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2111.14614

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',ρ,\mathcal P)-almost periodic functions and (\mathcal B, I',ρ,\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.

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