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

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.