Multi-dimensional ρ-almost periodic type functions and applications

Abstract

In this paper, we analyze various classes of multi-dimensional ρ-almost periodic type functions and multi-dimensional -almost periodic type functions , where , , X and Y are complex Banach spaces and ρ is a binary relation on Y. The proposed notion is new even in the one-dimensional setting, for the functions of the form . The main structural properties and characterizations for the introduced classes of functions are presented. We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations, as well.