Stability of an additive-quadratic functional equation in modular spaces
Using the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complete convex modular spaces satisfying Fatou property or Δ2{\Delta...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0075 |
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| author | Baza Abderrahman Rossafi Mohamed Park Choonkil Donganont Mana |
| author_facet | Baza Abderrahman Rossafi Mohamed Park Choonkil Donganont Mana |
| author_sort | Baza Abderrahman |
| collection | DOAJ |
| description | Using the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complete convex modular spaces satisfying Fatou property or Δ2{\Delta }_{2}-condition. |
| format | Article |
| id | doaj-art-fb83ca425f4f4e1189e17e812c3ec5c0 |
| institution | DOAJ |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-fb83ca425f4f4e1189e17e812c3ec5c02025-08-20T02:51:03ZengDe GruyterOpen Mathematics2391-54552024-11-0122126327910.1515/math-2024-0075Stability of an additive-quadratic functional equation in modular spacesBaza Abderrahman0Rossafi Mohamed1Park Choonkil2Donganont Mana3Department of Mathematics, Laboratory of Analysis, Geometry and Application, Ibn Tofail University, B.P. 133, Kenitra, MoroccoLaboratory Partial Differential Equations, Spectral Algebra and Geometry, Higher School of Education and Training, University Ibn Tofail, Kenitra, MoroccoResearch Institute for Convergence of Basic Sciences, Hanyang University, Seoul 04763, KoreaSchool of Science, University of Phayao, Phayao 56000, ThailandUsing the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complete convex modular spaces satisfying Fatou property or Δ2{\Delta }_{2}-condition.https://doi.org/10.1515/math-2024-0075hyers-ulam-rassias stabilityadditive-quadratic functional equationmodular spacefatou propertyδ2-condition39b8239b52 |
| spellingShingle | Baza Abderrahman Rossafi Mohamed Park Choonkil Donganont Mana Stability of an additive-quadratic functional equation in modular spaces Open Mathematics hyers-ulam-rassias stability additive-quadratic functional equation modular space fatou property δ2-condition 39b82 39b52 |
| title | Stability of an additive-quadratic functional equation in modular spaces |
| title_full | Stability of an additive-quadratic functional equation in modular spaces |
| title_fullStr | Stability of an additive-quadratic functional equation in modular spaces |
| title_full_unstemmed | Stability of an additive-quadratic functional equation in modular spaces |
| title_short | Stability of an additive-quadratic functional equation in modular spaces |
| title_sort | stability of an additive quadratic functional equation in modular spaces |
| topic | hyers-ulam-rassias stability additive-quadratic functional equation modular space fatou property δ2-condition 39b82 39b52 |
| url | https://doi.org/10.1515/math-2024-0075 |
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