In 1982, Fickett attempted to prove the Hyers-Ulam stability of isometries defined on a bounded subset of $ \mathbb{R}^n $. In this paper, we applied an intuitive and efficient approach to prove the Hyers-Ulam stability of isometries defined on the bounded subset of $ \mathbb{R}^4 $, and we significantly improved Fickett's theorem for the four-dimensional case.
Citation: Soon-Mo Jung, Jaiok Roh. Local stability of isometries on $ 4 $-dimensional Euclidean spaces[J]. AIMS Mathematics, 2024, 9(7): 18403-18416. doi: 10.3934/math.2024897
In 1982, Fickett attempted to prove the Hyers-Ulam stability of isometries defined on a bounded subset of $ \mathbb{R}^n $. In this paper, we applied an intuitive and efficient approach to prove the Hyers-Ulam stability of isometries defined on the bounded subset of $ \mathbb{R}^4 $, and we significantly improved Fickett's theorem for the four-dimensional case.
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Soon-Mo Jung, Jaiok Roh. Local stability of isometries on $ 4 $-dimensional Euclidean spaces[J]. AIMS Mathematics, 2024, 9(7): 18403-18416. doi: 10.3934/math.2024897
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