Comment on “Approximate ternary Jordan derivations on Banach ternary algebras” [Bavand Savadkouhi<i>et al.</i>J. Math. Phys. 50, 042303 (2009)]

Abstract

Let A be a Banach ternary algebra over C and X a ternary Banach A-module. A C-linear mapping D:(A,[ ]A)→(X,[ ]X) is called a ternary Jordan derivation if D([xxx]A)=[D(x)xx]X+[xD(x)x]X+[xxD(x)]X for all x∊A. [Bavand Savadkouhi et al., J. Math. Phys. 50, 042303 (2009)] investigated ternary Jordan derivations on Banach ternary algebras, associated with the following functional equation: f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)=2f(x), and proved the generalized Ulam–Hyers stability of ternary Jordan derivations on Banach ternary algebras. The mapping f in Lemma 2.2 of Bavand Savadkouhi et al. is identically zero and all of the results are trivial. In this note, we correct the statements of the results and the proofs.

Locations

• Journal of Mathematical Physics - View - PDF