Eshaghi Gordji, M.; Kaboli Gharetapeh, S.; Bavand Savadkouhi, M.; Aghaei, M.; Karimi, T. On cubic derivations. (English) Zbl 1236.39027 Int. J. Math. Anal., Ruse 4, No. 49-52, 2501-2514 (2010). Summary: We say a functional equation \((\xi)\) is stable if any function \(g\) satisfying the equation \((\xi)\) approximately is near to true solution of \((\xi)\). Also, we say that a functional equation is superstable if every approximately solution is an exact solution of it. In this paper, we investigate the stability and superstability of the system of functional equations \[ \begin{cases} f(xy)=x^3f(y)+f(x)y^3,\\ f(2x+y)+f(2x-y)=2f(x+y) +2f(x-y)+12f(x)\end{cases} \] on Banach algebras. Cited in 8 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges 46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras Keywords:Banach algebra; cubic functional equation; derivation; stability; superstability PDFBibTeX XMLCite \textit{M. Eshaghi Gordji} et al., Int. J. Math. Anal., Ruse 4, No. 49--52, 2501--2514 (2010; Zbl 1236.39027) Full Text: Link