On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces
In this paper, we investigate the stability of specially orthogonally functional equations deriving from additive and quadratic functions 4f(x+y)+4f(x−y)+10f(x)+14f(−x)−3f(y)−3f(−y)=f(2x+y)+f(2x−y) and f(x+y+z/2)+f(x+y−z/2)+f(x−y+z/2)+f(y+z−x/2)=f(x)+f(y)+f(z) where f is a mapping from Abelian group...
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| Format: | Article |
| Language: | English |
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Ada Academica
2024-05-01
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| Series: | European Journal of Mathematical Analysis |
| Online Access: | https://adac.ee/index.php/ma/article/view/233 |
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| author | Wenhui Xu Qi Liu Jinyu Xia |
| author_facet | Wenhui Xu Qi Liu Jinyu Xia |
| author_sort | Wenhui Xu |
| collection | DOAJ |
| description | In this paper, we investigate the stability of specially orthogonally functional equations deriving from additive and quadratic functions
4f(x+y)+4f(x−y)+10f(x)+14f(−x)−3f(y)−3f(−y)=f(2x+y)+f(2x−y)
and
f(x+y+z/2)+f(x+y−z/2)+f(x−y+z/2)+f(y+z−x/2)=f(x)+f(y)+f(z)
where f is a mapping from Abelian group to a non-Archimedean space. By adopting a new method, we have made an attempt to prove the Hyers-Ulam stability in non-Archimedean spaces. |
| format | Article |
| id | doaj-art-7a39e50826254d198d68ee7c53fbc0eb |
| institution | Kabale University |
| issn | 2733-3957 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Ada Academica |
| record_format | Article |
| series | European Journal of Mathematical Analysis |
| spelling | doaj-art-7a39e50826254d198d68ee7c53fbc0eb2024-12-22T12:23:47ZengAda AcademicaEuropean Journal of Mathematical Analysis2733-39572024-05-014111110.28924/ada/ma.4.11233On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean SpacesWenhui Xu0Qi Liu1Jinyu Xia2School of Mathematics and Physics, Anqing Normal University, Anqing 246133, P. R. ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, P. R. ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, P. R. ChinaIn this paper, we investigate the stability of specially orthogonally functional equations deriving from additive and quadratic functions 4f(x+y)+4f(x−y)+10f(x)+14f(−x)−3f(y)−3f(−y)=f(2x+y)+f(2x−y) and f(x+y+z/2)+f(x+y−z/2)+f(x−y+z/2)+f(y+z−x/2)=f(x)+f(y)+f(z) where f is a mapping from Abelian group to a non-Archimedean space. By adopting a new method, we have made an attempt to prove the Hyers-Ulam stability in non-Archimedean spaces.https://adac.ee/index.php/ma/article/view/233 |
| spellingShingle | Wenhui Xu Qi Liu Jinyu Xia On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces European Journal of Mathematical Analysis |
| title | On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces |
| title_full | On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces |
| title_fullStr | On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces |
| title_full_unstemmed | On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces |
| title_short | On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces |
| title_sort | on the stability of hyers orthogonality functional equations in non archimedean spaces |
| url | https://adac.ee/index.php/ma/article/view/233 |
| work_keys_str_mv | AT wenhuixu onthestabilityofhyersorthogonalityfunctionalequationsinnonarchimedeanspaces AT qiliu onthestabilityofhyersorthogonalityfunctionalequationsinnonarchimedeanspaces AT jinyuxia onthestabilityofhyersorthogonalityfunctionalequationsinnonarchimedeanspaces |