## 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.

Zbl 1112.39023
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