Hyers-Ulam stability of isometries on bounded domains
More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of Rn{{\mathbb{R}}}^{n} in 1981, Alestalo et al. [Isometric approximation, Israel J. Math. 125 (2001), 61–82] and Väisälä [Isometric approximation property in Euclidean spaces, Israe...
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| Format: | article |
| Langue: | EN |
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De Gruyter
2021
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| Accès en ligne: | https://doaj.org/article/303da22ab7f54314847dffa5c4cd0e73 |
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| Résumé: | More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of Rn{{\mathbb{R}}}^{n} in 1981, Alestalo et al. [Isometric approximation, Israel J. Math. 125 (2001), 61–82] and Väisälä [Isometric approximation property in Euclidean spaces, Israel J. Math. 128 (2002), 127] improved Fickett’s theorem significantly. In this paper, we will improve Fickett’s theorem by proving the Hyers-Ulam stability of isometries defined on bounded subsets of Rn{{\mathbb{R}}}^{n} using a more intuitive and more efficient approach that differs greatly from the methods used by Alestalo et al. and Väisälä. |
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