Comment to "Approximate bihomomorphisms and biderivations in 3-Lie algebras" [Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020]
- Authors
- Park, Choonkil; Gordji, Madjid Eshaghi; Targhi, Alireza Tavakkoli
- Issue Date
- May-2017
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Hyers-Ulam stability; biadditive mapping; C*-ternary algebra; bihomomorphism; biderivation
- Citation
- INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v.14, no.5
- Indexed
- SCIE
SCOPUS
- Journal Title
- INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
- Volume
- 14
- Number
- 5
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/152431
- DOI
- 10.1142/S0219887817500797
- ISSN
- 0219-8878
- Abstract
- Shokri et al. [Approximate bihomomorphisms and biderivations in 3-Lie algebras, Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020, 13pp.] 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 [J. Shokri, A. Ebadian and R. Aghalari, Approximate bihomomorphisms and biderivations in 3-Lie algebras, Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020, 13pp., Sec. 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 [J. Shokri, A. Ebadian and R. Aghalari, Approximate bihomomorphisms and biderivations in 3-Lie algebras, Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020, 13pp., Sec. 3], and prove the corrected theorems.
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