Geodesic
Approximate ternary quadratic derivation on ternary Banach algebras and $C^*$-ternary rings revisited
Park, Choonkill1 ; Lee, Jung Rye2
1 Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
2 Department of Mathematics, Daejin University, Kyeonggi 487-711, Korea
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 218-223.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Recently, Shagholi et al. [S. Shagholi, M. Eshaghi Gordji, M. B. Savadkouhi, J. Comput. Anal. Appl., 13 (2011), 1097-1105] defined ternary quadratic derivations on ternary Banach algebras and proved the Hyers-Ulam stability of ternary quadratic derivations on ternary Banach algebras. But the definition was not well-defined. Using the fixed point method, Bodaghi and Alias [A. Bodaghi, I. A. Alias, Adv. Difference Equ., 2012 (2012), 9 pages] proved the Hyers-Ulam stability and the superstability of ternary quadratic derivations on ternary Banach algebras and $C^*$-ternary rings. There are approximate $\mathbb{C}$-quadraticity conditions in the statements of the theorems and the corollaries, but the proofs for the $\mathbb{C}$-quadraticity were not completed. In this paper, we correct the definition of ternary quadratic derivation and complete the proofs of the theorems and the corollaries.
DOI : 10.22436/jnsa.008.03.05
Classification : 39B52, 13N15, 47H10, 47B47
Keywords: Hyers-Ulam stability, algebra- \(C^*\)-ternary ring, fixed point, quadratic functional equation, algebra-ternary Banach algebra, ternary quadratic derivation.

Park, Choonkill 1 ; Lee, Jung Rye 2

1 Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
2 Department of Mathematics, Daejin University, Kyeonggi 487-711, Korea 
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Park, Choonkill; Lee, Jung Rye. Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings revisited. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 218-223. doi : 10.22436/jnsa.008.03.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.03.05/

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