Comment to: “Approximate bihomomorphisms and biderivations in 3-Lie algebras”. (English) Zbl 1382.17005
Summary: J. Shokri et al. [ibid. 10, No. 1, Paper No. 1220020, 13 p. (2013; Zbl 1382.17006)] proved the Hyers-Ulam stability of bihomomorphisms and biderivations on normed 3-Lie algebras. It is easy to see that the definition of bihomomorphism in normed 3-Lie algebras is meaningless and so the results of [loc. cit., Section 3] are meaningless. Moreover, there is a serious problem in the main functional equation (1.2). So, we replace the functional equation (1.2) by a suitable functional equation. In this paper, we correct the definition of bihomomorphism and the statements of the results in [loc. cit., Section 3], and prove the corrected theorems.
MSC:
| 17A40 | Ternary compositions |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 39B82 | Stability, separation, extension, and related topics for functional equations |
Keywords:
Hyers-Ulam stability; biadditive mapping; \(C^\ast\)-ternary algebra; bihomomorphism; biderivationCitations:
Zbl 1382.17006References:
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