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

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 ( [ x x x ] A ) = [ D ( x ) x x ] X + [ x D ( x ) x ] X + [ x x D ( 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 ( ( 3 x − y − 4 z ) / 4 ) + f ( ( 4 x + 3 z ) / 4 ) = 2 f ( 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.