Generalized Almost Periodicity in Measure
Date Issued
2024
Author(s)
Marko Kostic, Wei-Shih Du, Halis Can Koyuncuoglu, Daniel Velinov
DOI
https://doi.org/10.3390/math12040548
Abstract
This paper investigates diverse classes of multidimensional Weyl and Doss ρ-almost
periodic functions in a general measure setting. This study establishes the fundamental structural
properties of these generalized ρ-almost periodic functions, extending previous classes such as
m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl p-almost periodic functions is introduced, where the exponent p > 0 is general. This paper delves
into the abstract Volterra integro-differential inclusions, showcasing the practical implications of
the derived results. This work builds upon the extensions made in the realm of Levitan N-almost
periodic functions, contributing to the broader understanding of mathematical functions in diverse
measure spaces.
periodic functions in a general measure setting. This study establishes the fundamental structural
properties of these generalized ρ-almost periodic functions, extending previous classes such as
m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl p-almost periodic functions is introduced, where the exponent p > 0 is general. This paper delves
into the abstract Volterra integro-differential inclusions, showcasing the practical implications of
the derived results. This work builds upon the extensions made in the realm of Levitan N-almost
periodic functions, contributing to the broader understanding of mathematical functions in diverse
measure spaces.
Subjects