APPROXIMATE BIHOMOMORPHISMS AND BIDERIVATIONS IN 3-LIE ALGEBRAS: REVISITED
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Shokri et al. [14] proved the Hyers-Ulam stability of bihomomorphisms and biderivations by using the direct method. It is easy to show that the de¯nition of biderivations on normed 3-Lie algebras is meaningless and so the results of [14] are meaningless. In this paper, we correct the de¯nition of biderivations and the statements of the results in [14], and prove the corrected theorems.
Abstract
Shokri et al. [14] proved the Hyers-Ulam stability of bihomomorphisms and biderivations by using the direct method. It is easy to show that the de¯nition of biderivations on normed 3-Lie algebras is meaningless and so the results of [14] are meaningless. In this paper, we correct the de¯nition of biderivations and the statements of the results in [14], and prove the corrected theorems.
참고문헌 (15)
- T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
- 배재형, "APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS", 대한수학회보, 47(1), pp.195~209 (2010), 대한수학회
- M. Eshaghi Gordji, "On the stability of quadratic double centralizers on Banach algebras", J. Comput. Anal. Appl, 13, pp.724~729 (2011)
- M. Eshaghi Gordji, "Nearly higher deriva-tions in unital C*-algebras", J. Comput. Anal. Appl, 13, pp.734~742 (2011)
- M. Eshaghi Gordji, "Generalized ternary bi-derivations on ternary Banach algebras: a fixed point approach", J. Comput. Anal. Appl, 15, pp.45~54 (2013)
- T. Hopkins, "Nilpotent ideals in Lie and anti-Lie triple systems", J. Algebra, 178, pp.480~492 (1995)
- D.H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
- W.G. Lister, "A structure theory of Lie triple systems", Trans. Amer. Math. Soc, 72, pp.217~242 (1952)
- M.S. Moslehian, "Almost derivations on C*-ternary rings", Bull. Belg. Math. Soc.-Simon Stevin, 14, pp.135~142 (2007)
- J.M. Rassias, "On approximation of approximately linear mappings by linear mappings", J. Funct. Anal, 46, pp.126~130 (1982)
- Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- S. Shagholi, "Stability of ternary quadratic derivations on ternary Banach algebras", J. Comput. Anal. Appl, 13, pp.1097~1105 (2011)
- S. Shagholi, "Nearly ternaty cubic homo-morphisms in ternary Frechet algebras", J. Comput. Anal. Appl, 13, pp.1106~1114 (2011)
- J. Shokri, "Approximate bihomomorphisms and bideriva-tions in 3-Lie algebras", Int. J. Geom. Methods Mod. Phys, 10(1), pp.13~ (2013)
- S.M. Ulam, "Problems in Modern Mathematics" (1940), Wiley