Almost periodic functions on Hausdorff almost periodic time scales
Abstract This paper is devoted to generalizing the notion of almost periodic functions on time scales. We introduce a new class of almost periodic time scales called Hausdorff almost periodic time scales by using the Hausdorff distance and propose a more general notion of almost periodic functions o...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1159-5 |
| _version_ | 1818250567836762112 |
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| author | Desheng Ji Liu Yang Jimin Zhang |
| author_facet | Desheng Ji Liu Yang Jimin Zhang |
| author_sort | Desheng Ji |
| collection | DOAJ |
| description | Abstract This paper is devoted to generalizing the notion of almost periodic functions on time scales. We introduce a new class of almost periodic time scales called Hausdorff almost periodic time scales by using the Hausdorff distance and propose a more general notion of almost periodic functions on these new time scales. Then we explore some properties of Hausdorff almost periodic time scales and prove that the family of almost periodic functions on Hausdorff almost periodic time scales is a Banach space. Especially, our analysis also indicates that a function on a Hausdorff almost periodic time scale is almost periodic if and only if its affine extension is Bohr almost periodic on the real numbers R ${\mathbb{R}}$ . As an application, we establish the existence of almost periodic solutions for a single species model on Hausdorff almost periodic time scales. |
| first_indexed | 2024-12-12T15:54:27Z |
| format | Article |
| id | doaj.art-2871645372da4bf0b7bdbc7493662a4a |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T15:54:27Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-2871645372da4bf0b7bdbc7493662a4a2022-12-22T00:19:31ZengSpringerOpenAdvances in Difference Equations1687-18472017-04-012017111410.1186/s13662-017-1159-5Almost periodic functions on Hausdorff almost periodic time scalesDesheng Ji0Liu Yang1Jimin Zhang2School of Mathematical Sciences, Heilongjiang UniversityCollege of Automation, Harbin Engineering UniversitySchool of Mathematical Sciences, Heilongjiang UniversityAbstract This paper is devoted to generalizing the notion of almost periodic functions on time scales. We introduce a new class of almost periodic time scales called Hausdorff almost periodic time scales by using the Hausdorff distance and propose a more general notion of almost periodic functions on these new time scales. Then we explore some properties of Hausdorff almost periodic time scales and prove that the family of almost periodic functions on Hausdorff almost periodic time scales is a Banach space. Especially, our analysis also indicates that a function on a Hausdorff almost periodic time scale is almost periodic if and only if its affine extension is Bohr almost periodic on the real numbers R ${\mathbb{R}}$ . As an application, we establish the existence of almost periodic solutions for a single species model on Hausdorff almost periodic time scales.http://link.springer.com/article/10.1186/s13662-017-1159-5time scalesHausdorff almost periodic time scalesalmost periodic functions on time scalesHausdorff distanceBohr almost periodic functions |
| spellingShingle | Desheng Ji Liu Yang Jimin Zhang Almost periodic functions on Hausdorff almost periodic time scales Advances in Difference Equations time scales Hausdorff almost periodic time scales almost periodic functions on time scales Hausdorff distance Bohr almost periodic functions |
| title | Almost periodic functions on Hausdorff almost periodic time scales |
| title_full | Almost periodic functions on Hausdorff almost periodic time scales |
| title_fullStr | Almost periodic functions on Hausdorff almost periodic time scales |
| title_full_unstemmed | Almost periodic functions on Hausdorff almost periodic time scales |
| title_short | Almost periodic functions on Hausdorff almost periodic time scales |
| title_sort | almost periodic functions on hausdorff almost periodic time scales |
| topic | time scales Hausdorff almost periodic time scales almost periodic functions on time scales Hausdorff distance Bohr almost periodic functions |
| url | http://link.springer.com/article/10.1186/s13662-017-1159-5 |
| work_keys_str_mv | AT deshengji almostperiodicfunctionsonhausdorffalmostperiodictimescales AT liuyang almostperiodicfunctionsonhausdorffalmostperiodictimescales AT jiminzhang almostperiodicfunctionsonhausdorffalmostperiodictimescales |