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Comment to "Approximate bihomomorphisms and biderivations in 3-Lie algebras" [Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020]

Title
Comment to "Approximate bihomomorphisms and biderivations in 3-Lie algebras" [Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020]
Author
박춘길
Keywords
Hyers-Ulam stability; biadditive mapping; C*-ternary algebra; bihomomorphism; biderivation
Issue Date
2017-05
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Citation
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v. 14, no. 5, Article no. 1750079
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.
URI
https://www.worldscientific.com/doi/abs/10.1142/S0219887817500797https://repository.hanyang.ac.kr/handle/20.500.11754/114158
ISSN
0219-8878; 1793-6977
DOI
10.1142/S0219887817500797
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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