Stability of bi-theta-derivations on JB*-triples: Revisited

Abstract

Ebadian et al. [Stability of bi-theta-derivations on JB*-triples, Int. J. Geom. Meth. Mod. Phys. 9(7) (2012) 1250051, 12 pp.] proved the Hyers-Ulam stability of bi-theta-derivations on JB*-triples. Under the conditions of the definition of bi-theta-derivation given in the above paper, the bi-theta-derivation must be zero. So the results given in the above paper must be trivial. Under the conditions in the main theorem, we can show that the related mapping must be zero. In this paper, we correct the statements of the results and prove the corrected theorems and corollaries.