Hyers-Ulam stability of isometries on bounded domains-II

• Autorzy: Choi, Ginkyu , Jung, Soon-Mo
• Języki publikacji: EN

Abstrakty

EN

The question of whether there is a true isometry approximating the ε -isometry defined in the bounded subset of the n -dimensional Euclidean space has long been considered an interesting question. In 1982, Fickett published the first article on this topic, and in early 2000, Alestalo et al. and Väisälä improved Fickett’s result significantly. Recently, the second author of this article published a paper improving the previous results. The main purpose of this article is to significantly improve all of the aforementioned results by applying a basic and intuitive method.

Słowa kluczowe

PL

izometria; stabilność Hyersa-Ulama

EN

isometry; ε-isometry; Hyers-Ulam stability; bounded domain

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: 1--12
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Choi, Ginkyu

• Department of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea,

autor

Jung, Soon-Mo

• Mathematics Section, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea,

Bibliografia

• [1] D. H. Hyers and S. M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288–292.
• [2] D. G. Bourgin, Approximate isometries, Bull. Amer. Math. Soc. 52 (1946), 704–714.
• [3] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385–397.
• [4] R. D. Bourgin, Approximate isometries on finite dimensional Banach spaces, Trans. Amer. Math. Soc. 207 (1975), 309–328.
• [5] L. Cheng, Q. Cheng, K. Tu and J. Zhang, A universal theorem for stability of ε-isometries of Banach spaces, J. Funct. Anal. 269 (2015), no. 1, 199–214.
• [6] L. Cheng and Y. Dong, A note on the stability of nonsurjective ε-isometries of Banach spaces, Proc. Amer. Math. Soc. 148 (2020), 4837–4844.
• [7] J. Gevirtz, Stability of isometries on Banach spaces, Proc. Amer. Math. Soc. 89 (1983), 633–636.
• [8] P. M. Gruber, Stability of isometries, Trans. Amer. Math. Soc. 245 (1978), 263–277.
• [9] D. H. Hyers and S. M. Ulam, Approximate isometries of the space of continuous functions, Ann. Math. 48 (1947), 285–289.
• [10] M. Omladicccc and P. SSSemrl, On non linear perturbations of isometries, Math. Ann. 303 (1995), 617–628.
• [11] I. A. Vestfrid, Stability of almost surjective ε-isometries of Banach spaces, J. Funct. Anal. 269 (2015), no. 7, 2165–2170.
• [12] I. A. Vestfrid, Hyers-Ulam stability of isometries and non-expansive maps between spaces of continuous functions, Proc. Amer. Math. Soc. 145 (2017), 2481–2494.
• [13] J. W. Fickett, Approximate isometries on bounded sets with an application to measure theory, Studia Math. 72 (1982), 37–46.
• [14] P. Alestalo, D. A. Trotsenko and J. Väisälä, Isometric approximation, Israel J. Math. 125 (2001), 61–82.
• [15] J. Väisälä, Isometric approximation property in Euclidean spaces, Israel J. Math. 128 (2002), 1–27.
• [16] S.-M. Jung, Hyers-Ulam stability of isometries on bounded domains, Open Math. 19 (2021), no. 1, 675–689.
• [17] S.-M. Jung, J. Roh and D.-J. Yang, On the improvement of Fickettas theorem on bounded sets, J. Inequ. Appl. 2022 (2022), no. 17, 13.
• [18] I. A. Vestfrid, ε-Isometries in Euclidean spaces, Nonlinear Anal. 63 (2005), 1191–1198.

Identyfikatory

DOI

10.1515/dema-2022-0196