Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras
In this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></mat...
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2025-07-01
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| author | Jae-Hyeong Bae Won-Gil Park |
| author_facet | Jae-Hyeong Bae Won-Gil Park |
| author_sort | Jae-Hyeong Bae |
| collection | DOAJ |
| description | In this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-ternary algebras. The study of functional equations with a sufficient number of variables can be helpful in solving real-world problems such as artificial intelligence. In this paper, we build on previous research on functional equations with four variables to study functional equations with as many variables as desired. We introduce new bounds for the stability of mappings satisfying generalized bi-additive conditions and demonstrate the uniqueness of approximating bi-isomorphisms. The results contribute to the deeper understanding of ternary algebraic structures and related functional equations, relevant to both pure mathematics and quantum information science. |
| format | Article |
| id | doaj-art-9712e73b410a46ed9c8a9f42c3eee194 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9712e73b410a46ed9c8a9f42c3eee1942025-08-20T03:36:14ZengMDPI AGMathematics2227-73902025-07-011314228910.3390/math13142289Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary AlgebrasJae-Hyeong Bae0Won-Gil Park1School of Liberal Studies, Kyung Hee University, Yongin 17104, Republic of KoreaDepartment of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of KoreaIn this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-ternary algebras. The study of functional equations with a sufficient number of variables can be helpful in solving real-world problems such as artificial intelligence. In this paper, we build on previous research on functional equations with four variables to study functional equations with as many variables as desired. We introduce new bounds for the stability of mappings satisfying generalized bi-additive conditions and demonstrate the uniqueness of approximating bi-isomorphisms. The results contribute to the deeper understanding of ternary algebraic structures and related functional equations, relevant to both pure mathematics and quantum information science.https://www.mdpi.com/2227-7390/13/14/2289<i>C</i>*-ternary algebrabi-homomorphismbi-derivationbi-isomorphismfunctional equation |
| spellingShingle | Jae-Hyeong Bae Won-Gil Park Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras Mathematics <i>C</i>*-ternary algebra bi-homomorphism bi-derivation bi-isomorphism functional equation |
| title | Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras |
| title_full | Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras |
| title_fullStr | Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras |
| title_full_unstemmed | Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras |
| title_short | Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in <i>C</i>*-Ternary Algebras |
| title_sort | generalized hyers ulam stability of bi homomorphisms bi derivations and bi isomorphisms in i c i ternary algebras |
| topic | <i>C</i>*-ternary algebra bi-homomorphism bi-derivation bi-isomorphism functional equation |
| url | https://www.mdpi.com/2227-7390/13/14/2289 |
| work_keys_str_mv | AT jaehyeongbae generalizedhyersulamstabilityofbihomomorphismsbiderivationsandbiisomorphismsiniciternaryalgebras AT wongilpark generalizedhyersulamstabilityofbihomomorphismsbiderivationsandbiisomorphismsiniciternaryalgebras |