Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in C *-Ternary Algebras

Jae-Hyeong Bae and Won-Gil Park ()
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Jae-Hyeong Bae: School of Liberal Studies, Kyung Hee University, Yongin 17104, Republic of Korea
Won-Gil Park: Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea

Mathematics, 2025, vol. 13, issue 14, 1-13

Abstract: In this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in C * -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.

Keywords: C *-ternary algebra; bi-homomorphism; bi-derivation; bi-isomorphism; functional equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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