Almost periodic and asymptotically almost periodic functions: part I
Abstract In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces. Special accent is put on the Stepanov generalizations of almost periodic functions and asymptotically almost periodic functions...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-02-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1487-0 |
| _version_ | 1818128285151789056 |
|---|---|
| author | Dhaou Lassoued Rahim Shah Tongxing Li |
| author_facet | Dhaou Lassoued Rahim Shah Tongxing Li |
| author_sort | Dhaou Lassoued |
| collection | DOAJ |
| description | Abstract In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces. Special accent is put on the Stepanov generalizations of almost periodic functions and asymptotically almost periodic functions. We also recollect some basic results regarding equi-Weyl-almost periodic functions and Weyl-almost periodic functions. The class of asymptotically Weyl-almost periodic functions, introduced in this work, seems to be not considered elsewhere even in the scalar-valued case. We actually introduce eight new classes of asymptotically almost periodic functions and analyze relations between them. In order to make a picture as complete and clear as possible, several illustrating examples and counter-examples are given. It is worth noting that the topics dealt with in this paper seem to be of an intrinsic connection with the problem of existence and uniqueness of solutions of differential and difference equations, in both determinist and stochastic cases. |
| first_indexed | 2024-12-11T07:30:49Z |
| format | Article |
| id | doaj.art-013a1a9a86c4454d9df8b8dac1c280f9 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T07:30:49Z |
| publishDate | 2018-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-013a1a9a86c4454d9df8b8dac1c280f92022-12-22T01:15:49ZengSpringerOpenAdvances in Difference Equations1687-18472018-02-012018111910.1186/s13662-018-1487-0Almost periodic and asymptotically almost periodic functions: part IDhaou Lassoued0Rahim Shah1Tongxing Li2Département de Mathématiques, Faculté des Sciences de Gabès, Université de GabèsDepartment of Mathematics, University of PeshawarLinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi UniversityAbstract In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces. Special accent is put on the Stepanov generalizations of almost periodic functions and asymptotically almost periodic functions. We also recollect some basic results regarding equi-Weyl-almost periodic functions and Weyl-almost periodic functions. The class of asymptotically Weyl-almost periodic functions, introduced in this work, seems to be not considered elsewhere even in the scalar-valued case. We actually introduce eight new classes of asymptotically almost periodic functions and analyze relations between them. In order to make a picture as complete and clear as possible, several illustrating examples and counter-examples are given. It is worth noting that the topics dealt with in this paper seem to be of an intrinsic connection with the problem of existence and uniqueness of solutions of differential and difference equations, in both determinist and stochastic cases.http://link.springer.com/article/10.1186/s13662-018-1487-0almost periodic functionasymptotically almost periodic function |
| spellingShingle | Dhaou Lassoued Rahim Shah Tongxing Li Almost periodic and asymptotically almost periodic functions: part I Advances in Difference Equations almost periodic function asymptotically almost periodic function |
| title | Almost periodic and asymptotically almost periodic functions: part I |
| title_full | Almost periodic and asymptotically almost periodic functions: part I |
| title_fullStr | Almost periodic and asymptotically almost periodic functions: part I |
| title_full_unstemmed | Almost periodic and asymptotically almost periodic functions: part I |
| title_short | Almost periodic and asymptotically almost periodic functions: part I |
| title_sort | almost periodic and asymptotically almost periodic functions part i |
| topic | almost periodic function asymptotically almost periodic function |
| url | http://link.springer.com/article/10.1186/s13662-018-1487-0 |
| work_keys_str_mv | AT dhaoulassoued almostperiodicandasymptoticallyalmostperiodicfunctionsparti AT rahimshah almostperiodicandasymptoticallyalmostperiodicfunctionsparti AT tongxingli almostperiodicandasymptoticallyalmostperiodicfunctionsparti |