C ∗ $$C^*$$ -Bi-Ternary Derivations in C ∗ $$C^*$$ -Algebra-Ternary Algebras

Jung Rye Lee (), Choonkil Park () and Michael Th. Rassias
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Jung Rye Lee: Daejin University, Department of Data Science
Choonkil Park: Hanyang University, Department of Mathematics
Michael Th. Rassias: Hellenic Military Academy, Department of Mathematics and Engineering Sciences

A chapter in Functional Equations and Ulam’s Problem, 2026, pp 303-325 from Springer

Abstract: Abstract We introduce the following additive functional equation 1 g ( λu + v + 2 y ) = λg ( u ) + g ( v ) + 2 g ( y ) $$\displaystyle \begin{aligned} {} g(\lambda u +v+ 2y)= \lambda g(u) + g(v) + 2 g(y) \end{aligned} $$ for all λ ∈ C $$\lambda \in \mathbf {C}$$ , all unitary elements u , v $$u, v$$ in a unital C ∗ $$C^*$$ -algebra-ternary algebra P and all y ∈ P $$y\in P$$ . Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the additive functional equation ( 1 ) in unital C ∗ $$C^*$$ -algebra-ternary algebras. Furthermore, we apply to study C ∗ $$C^*$$ -bi-ternary homomorphisms and C ∗ $$C^*$$ -bi-ternary derivations in unital C ∗ $$C^*$$ -algebra-ternary algebras.

Date: 2026
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DOI: 10.1007/978-3-032-08949-6_14

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