Generalized Almost Periodicity in Measure

Marko Kostić, Wei-Shih Du (), Halis Can Koyuncuoğlu and Daniel Velinov
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Marko Kostić: Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Wei-Shih Du: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Halis Can Koyuncuoğlu: Department of Engineering Sciences, Izmir Katip Celebi University, Izmir 35620, Turkey
Daniel Velinov: Department for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje, Partizanski Odredi 24, P.O. Box 560, 1000 Skopje, North Macedonia

Mathematics, 2024, vol. 12, issue 4, 1-14

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.

Keywords: Weyl ?-almost periodic functions; Doss ?-almost periodic functions; general measure; convolution products; Volterra integro-differential inclusions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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