New contributions on asymptotically periodic functions and 𝒮-asymptotically omega periodic functions

Abstract

In this work, we establish some new results on Asymptotically periodic functions and $\mathcal{S}$-Asymptotically omega periodic functions. The obtained results is the extension of those established recently in the literature. Then we establish many interesting results on those functions, namely their characterization, we give also the sufficient conditions under which their primitive remain in the same space. The existence of mean value for such functions. All sections are illustrated by examples or counter examples.

Keywords:

• Asymptotically periodic functions
• $\mathcal{S}$-asymptotically omega periodic function
• subgroup
• mean value
• relative compactness of range
• primitive

MSC:

• 34K14
• 34A45
• 47D06

Acknowledgments

The authors would like to express their thanks to the editor and anonymous referees for his/her suggestions and comments that improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).