Stability of Tri-Homomorphisms, Tri-Derivations, and Tri-Isomorphisms in C*-Ternary Algebras
Abstract
1. Introduction and Background
- (i)
- ;
- (ii)
- ;
- (iii)
- .
- (i)
- The mapping τ acts -linearly on the first and third variables.
- (ii)
- On the second variable, τ is conjugate -linear.
- (iii)
- τ is associative in the sense that, for every and every ,
2. Stability of Tri-Homomorphisms in -Ternary Algebras
3. Stability of Tri-Derivations and Tri-Isomorphisms in -Ternary Algebras
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Cayley, A. On the 34 concomitants of the ternary cubic. Am. J. Math. 1881, 4, 1–15. [Google Scholar] [CrossRef]
- Zettl, H. A characterization of ternary rings of operators. Adv. Math. 1983, 48, 117–143. [Google Scholar] [CrossRef]
- Moslehian, M.S. Almost derivations on C*-ternary rings. Bull. Belg. Math. Soc.–Simon Stevin 2007, 14, 135–142. [Google Scholar] [CrossRef]
- Bae, J.-H.; Park, W.-G. Generalized Ulam-Hyers stability of C*-ternary algebra 3-homomorphisms for a functional equation. J. Chungcheong Math. Soc. 2011, 24, 147–162. [Google Scholar]
- Dehghanian, M.; Mosadegh, S.M.S.M.; Park, C.; Shin, D.Y. C*-ternary 3-derivations on C*-ternary algebras. J. Inequal. Appl. 2013, 2013, 124. [Google Scholar] [CrossRef]
- Ulam, S.M. A Collection of Mathematical Problems; Interscience: New York, NY, USA, 1960. [Google Scholar]
- Hyers, D.H. On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 1941, 27, 222–224. [Google Scholar] [CrossRef] [PubMed]
- Aoki, T. On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 1950, 2, 64–66. [Google Scholar] [CrossRef]
- Rassias, T.M. On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 1978, 72, 297–300. [Google Scholar] [CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Bae, J.-H.; Park, W.-G. Stability of Tri-Homomorphisms, Tri-Derivations, and Tri-Isomorphisms in C*-Ternary Algebras. Mathematics 2025, 13, 3156. https://doi.org/10.3390/math13193156
Bae J-H, Park W-G. Stability of Tri-Homomorphisms, Tri-Derivations, and Tri-Isomorphisms in C*-Ternary Algebras. Mathematics. 2025; 13(19):3156. https://doi.org/10.3390/math13193156
Chicago/Turabian StyleBae, Jae-Hyeong, and Won-Gil Park. 2025. "Stability of Tri-Homomorphisms, Tri-Derivations, and Tri-Isomorphisms in C*-Ternary Algebras" Mathematics 13, no. 19: 3156. https://doi.org/10.3390/math13193156
APA StyleBae, J.-H., & Park, W.-G. (2025). Stability of Tri-Homomorphisms, Tri-Derivations, and Tri-Isomorphisms in C*-Ternary Algebras. Mathematics, 13(19), 3156. https://doi.org/10.3390/math13193156