Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations
The aim of this work is to give sufficient conditions ensuring that the space PAP(, X, µ) of µ-pseudo almost periodic functions and the space PAA(, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(). These results establish sufficient assum...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-06-01
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| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/msds-2020-0102 |
| _version_ | 1819009442949103616 |
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| author | Béssémè Fritz Mbounja Békollè David Ezzinbi Khalil Fatajou Samir Danga Duplex Elvis Houpa |
| author_facet | Béssémè Fritz Mbounja Békollè David Ezzinbi Khalil Fatajou Samir Danga Duplex Elvis Houpa |
| author_sort | Béssémè Fritz Mbounja |
| collection | DOAJ |
| description | The aim of this work is to give sufficient conditions ensuring that the space PAP(, X, µ) of µ-pseudo almost periodic functions and the space PAA(, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(). These results establish sufficient assumptions on k and the measure µ. As a consequence, we investigate the existence and uniqueness of µ-pseudo almost periodic solutions and µ-pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations. |
| first_indexed | 2024-12-21T00:56:27Z |
| format | Article |
| id | doaj.art-868e773a53ff4ac1a41383097858b313 |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-12-21T00:56:27Z |
| publishDate | 2020-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-868e773a53ff4ac1a41383097858b3132022-12-21T19:21:17ZengDe GruyterNonautonomous Dynamical Systems2353-06262020-06-0171325210.1515/msds-2020-0102msds-2020-0102Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equationsBéssémè Fritz Mbounja0Békollè David1Ezzinbi Khalil2Fatajou Samir3Danga Duplex Elvis Houpa4Département des Mathématiques Appliquées et Informatique, Ecole de Géologie et d’Exploitation Minière de Meiganga, Université de Ngaoundéré, B.P. 115 CamerounDépartement de Mathématiques et Informatique, Faculté des Sciences, Université de Ngaoundéré, B.P. 454 CamerounDépartement de Mathématiques, Faculté des Sciences Semlalia, Université Cadi-Ayyad, B.P. 2390 Marrakesh, MoroccoDépartement de Mathématiques et Informatique, Faculté Polydisciplinaire Sa˝„Université Cadi-Ayyad, Sidi Bouzid B.P.4162, MoroccoDépartement de Mathématiques et Informatique, Faculté des Sciences, Université de Ngaoundéré, B.P. 454 CamerounThe aim of this work is to give sufficient conditions ensuring that the space PAP(, X, µ) of µ-pseudo almost periodic functions and the space PAA(, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(). These results establish sufficient assumptions on k and the measure µ. As a consequence, we investigate the existence and uniqueness of µ-pseudo almost periodic solutions and µ-pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations.https://doi.org/10.1515/msds-2020-0102measure theoryµ-ergodicµ-pseudo almost periodic functionsµ-pseudo almost automorphic functionsintegral equationsevolution equationspartial functional differential equationsreaction-diffusion systems34c2734k1435b1535k5737a30 |
| spellingShingle | Béssémè Fritz Mbounja Békollè David Ezzinbi Khalil Fatajou Samir Danga Duplex Elvis Houpa Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations Nonautonomous Dynamical Systems measure theory µ-ergodic µ-pseudo almost periodic functions µ-pseudo almost automorphic functions integral equations evolution equations partial functional differential equations reaction-diffusion systems 34c27 34k14 35b15 35k57 37a30 |
| title | Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations |
| title_full | Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations |
| title_fullStr | Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations |
| title_full_unstemmed | Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations |
| title_short | Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations |
| title_sort | convolutions in µ pseudo almost periodic and µ pseudo almost automorphic function spaces and applications to solve integral equations |
| topic | measure theory µ-ergodic µ-pseudo almost periodic functions µ-pseudo almost automorphic functions integral equations evolution equations partial functional differential equations reaction-diffusion systems 34c27 34k14 35b15 35k57 37a30 |
| url | https://doi.org/10.1515/msds-2020-0102 |
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