On the improvement of Fickett’s theorem on bounded sets
Abstract Fickett proved the stability of isometries on bounded subsets of R n $\mathbb{R}^{n}$ for n ≥ 2 $n \ge 2$ . Jung then improved Fickett’s theorem for n ≥ 3 $n \ge 3$ . In this paper, we improve Fickett’s theorem for n = 2 $n = 2$ and improve Jung’s result for n = 3 $n = 3$ , by employing a f...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-01-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02752-w |
| _version_ | 1818954048499351552 |
|---|---|
| author | Soon-Mo Jung Jaiok Roh Dae-Jeong Yang |
| author_facet | Soon-Mo Jung Jaiok Roh Dae-Jeong Yang |
| author_sort | Soon-Mo Jung |
| collection | DOAJ |
| description | Abstract Fickett proved the stability of isometries on bounded subsets of R n $\mathbb{R}^{n}$ for n ≥ 2 $n \ge 2$ . Jung then improved Fickett’s theorem for n ≥ 3 $n \ge 3$ . In this paper, we improve Fickett’s theorem for n = 2 $n = 2$ and improve Jung’s result for n = 3 $n = 3$ , by employing a fundamental analytic method, as it can be used to explain mathematically many practical engineering problems. |
| first_indexed | 2024-12-20T10:15:58Z |
| format | Article |
| id | doaj.art-81dfc884572b497ea2ef3d11abf5c2fe |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-20T10:15:58Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-81dfc884572b497ea2ef3d11abf5c2fe2022-12-21T19:44:03ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-01-012022111310.1186/s13660-022-02752-wOn the improvement of Fickett’s theorem on bounded setsSoon-Mo Jung0Jaiok Roh1Dae-Jeong Yang2Mathematics Section, College of Science and Technology, Hongik UniversityIlsong College of Liberal Arts, Hallym UniversitySchool of Materials Science and Engineering, Hongik UniversityAbstract Fickett proved the stability of isometries on bounded subsets of R n $\mathbb{R}^{n}$ for n ≥ 2 $n \ge 2$ . Jung then improved Fickett’s theorem for n ≥ 3 $n \ge 3$ . In this paper, we improve Fickett’s theorem for n = 2 $n = 2$ and improve Jung’s result for n = 3 $n = 3$ , by employing a fundamental analytic method, as it can be used to explain mathematically many practical engineering problems.https://doi.org/10.1186/s13660-022-02752-wFickett’s theoremHyers–Ulam stabilityε-isometryIsometry |
| spellingShingle | Soon-Mo Jung Jaiok Roh Dae-Jeong Yang On the improvement of Fickett’s theorem on bounded sets Journal of Inequalities and Applications Fickett’s theorem Hyers–Ulam stability ε-isometry Isometry |
| title | On the improvement of Fickett’s theorem on bounded sets |
| title_full | On the improvement of Fickett’s theorem on bounded sets |
| title_fullStr | On the improvement of Fickett’s theorem on bounded sets |
| title_full_unstemmed | On the improvement of Fickett’s theorem on bounded sets |
| title_short | On the improvement of Fickett’s theorem on bounded sets |
| title_sort | on the improvement of fickett s theorem on bounded sets |
| topic | Fickett’s theorem Hyers–Ulam stability ε-isometry Isometry |
| url | https://doi.org/10.1186/s13660-022-02752-w |
| work_keys_str_mv | AT soonmojung ontheimprovementoffickettstheoremonboundedsets AT jaiokroh ontheimprovementoffickettstheoremonboundedsets AT daejeongyang ontheimprovementoffickettstheoremonboundedsets |