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**Homomorphisms and derivations in \(C^{\ast}\)-ternary algebras.**
*(English)*
Zbl 1169.39304

Summary: C. Park [J. Math. Phys. 47, No. 10, 103512 (2006; Zbl 1112.39023)] proved the stability of homomorphisms in \(C^{\ast }\)-ternary algebras and of derivations on \(C^{\ast }\)-ternary algebras for the following generalized Cauchy-Jensen additive mapping: \(2f((\sum_{j=1}^{p} x_{j}/2)+\sum_{j=1}^d y_j) = \sum^p_{j=1} f(x_j)+2\sum^d_{j=1}f(y_j)\). In this note, we improve and generalize some results concerning this functional equation.

### MSC:

39B52 | Functional equations for functions with more general domains and/or ranges |

39B82 | Stability, separation, extension, and related topics for functional equations |

46K70 | Nonassociative topological algebras with an involution |

47B47 | Commutators, derivations, elementary operators, etc. |

### Citations:

Zbl 1112.39023
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\textit{A. Najati} et al., Abstr. Appl. Anal. 2009, Article ID 612392, 16 p. (2009; Zbl 1169.39304)

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