Hyers–Ulam Stability of Isometries on Bounded Domains–III

The question of whether there is a true isometry that approximates the ε-isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al., Väisälä and Vestfrid. Recently, th...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-06, Vol.12 (12), p.1784
Main Authors: Choi, Ginkyu, Jung, Soon-Mo
Format: Article
Language:English
Subjects:
Analysis
bounded domain
Euclidean geometry
Euclidean space
Hyers–Ulam stability
Inequality
isometry
Mathematicians
Stability
Transformations (Mathematics)
ε-isometry
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Summary:The question of whether there is a true isometry that approximates the ε-isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al., Väisälä and Vestfrid. Recently, the authors published some papers improving the previous results. The main purpose of this paper is to improve all of the abovementioned results by utilizing the properties of the norm and inner product for Euclidean space.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12121784