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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Autor principal:	Jung Soon-Mo
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	isometry ε-isometry hyers-ulam stability bounded domain 39b82 46b04 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/303da22ab7f54314847dffa5c4cd0e73
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id	oai:doaj.org-article:303da22ab7f54314847dffa5c4cd0e73
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spelling	oai:doaj.org-article:303da22ab7f54314847dffa5c4cd0e732021-12-05T14:10:53ZHyers-Ulam stability of isometries on bounded domains2391-545510.1515/math-2021-0063https://doaj.org/article/303da22ab7f54314847dffa5c4cd0e732021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0063https://doaj.org/toc/2391-5455More 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.Jung Soon-MoDe Gruyterarticleisometryε-isometryhyers-ulam stabilitybounded domain39b8246b04MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 675-689 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	isometry ε-isometry hyers-ulam stability bounded domain 39b82 46b04 Mathematics QA1-939
spellingShingle	isometry ε-isometry hyers-ulam stability bounded domain 39b82 46b04 Mathematics QA1-939 Jung Soon-Mo Hyers-Ulam stability of isometries on bounded domains
description	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.
format	article
author	Jung Soon-Mo
author_facet	Jung Soon-Mo
author_sort	Jung Soon-Mo
title	Hyers-Ulam stability of isometries on bounded domains
title_short	Hyers-Ulam stability of isometries on bounded domains
title_full	Hyers-Ulam stability of isometries on bounded domains
title_fullStr	Hyers-Ulam stability of isometries on bounded domains
title_full_unstemmed	Hyers-Ulam stability of isometries on bounded domains
title_sort	hyers-ulam stability of isometries on bounded domains
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/303da22ab7f54314847dffa5c4cd0e73
work_keys_str_mv	AT jungsoonmo hyersulamstabilityofisometriesonboundeddomains
_version_	1718371594430054400

Hyers-Ulam stability of isometries on bounded domains

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