Choonkill Park - Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea. Jung Rye Lee - Department of Mathematics, Daejin University, Kyeonggi 487-711, Korea.
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.
Choonkill Park, Jung Rye Lee, Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings revisited, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 3, 218--223
Park Choonkill, Lee Jung Rye, Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings revisited. J. Nonlinear Sci. Appl. (2015); 8(3):218--223
Park, Choonkill, Lee, Jung Rye. "Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings revisited." Journal of Nonlinear Sciences and Applications, 8, no. 3 (2015): 218--223
