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Zbl 1236.39027
Eshaghi Gordji, M.; Kaboli Gharetapeh, S.; Bavand Savadkouhi, M.; Aghaei, M.; Karimi, T.
On cubic derivations. (English)
[J] Int. J. Math. Anal., Ruse 4, No. 49-52, 2501-2514 (2010). ISSN 1312-8876; ISSN 1314-7579/e

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 $$\cases f(xy)=x^3f(y)+f(x)y^3,\\ f(2x+y)+f(2x-y)=2f(x+y) +2f(x-y)+12f(x)\endcases$$ on Banach algebras.

MSC 2000:: *39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains
46L57 Derivations etc. in $C^*$-algebras

Keywords: Banach algebra; cubic functional equation; derivation; stability; superstability

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