Asymptotically ρ-almost periodic type functions in general metric

Abstract

In this paper, we analyze various classes of multi-dimensional asymptotically ρ-almost periodic type functions in general metric. We clarify the main structural properties for the introduced classes of asymptotically ρ-almost periodic type functions, and provide some applications of our results to the abstract Volterra integro-differential equations.

Generalized ρ-Almost Periodic Sequences and Applications

“…Let us finally mention some conclusions and final remarks about the introduced notion, some topics not considered here and some perspectives for further expansion of the theory. Before proceeding any further, we would like to emphasize that many other classes of generalized ρ-almost periodic type sequences are introduced and analyzed in our recent research studies [22][23][24][25]48,49]. For example, suppose that F : I × X → Y and (1) holds.…”

“…In particular, we introduce and analyze several new classes of Stepanov, Weyl, Besicovitch and Doss ρ-almost periodic-type sequences. Following our research studies carried out in [22][23][24][25], we can further analyze many other classes of multi-dimensional ρ-almost periodic-type sequences of the above form. The organization of paper can be briefly described as follows.…”