an:05839633 Zbl 1217.39034 Eshaghi Gordji, M.; Ghobadipour, N. Stability of $$(\alpha,\beta,\gamma)$$-derivatives on Lie $$C^*$$-algebras EN Int. J. Geom. Methods Mod. Phys. 7, No. 7, 1093-1102 (2010). 0219-8878 1793-6977 2010
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39B82 39B52 46K70 46L57 17B40 17B60 $$(\alpha , \beta , \gamma )$$-derivation; Lie $$C^*$$-algebra; Hyers-Ulam-Rassias stability; functional equation The authors investigate the stability of $$(\alpha, \beta, \gamma)$$-derivations on a Lie C*-algebra $$A$$ associated to the following functional equation $f\left(\frac{x_2-x_1}{3}\right)+f\left( \frac{x_1-3x_3}{3}\right) +f\left( \frac{3x_1+3x_3-x_2}{3}\right)=f(x_1).\tag{1}$ An $$(\alpha, \beta, \gamma)$$-derivation of $$A$$ is a linear map $$d:A \to A$$ such that for certain $$\alpha, \beta, \gamma \in {\mathbb C}$$ the identity $\alpha d[x,y]= \beta [d(x),y]+ \gamma [x, d(y)],$ for every $$x,y\in A$$ ($$[\;, \;]$$ denotes the Lie bracket of $$A$$). They show that if $$f$$ is an approximate solution of (1) (in the sense of the norm of $$A$$), then there exists a unique $$(\alpha, \beta, \gamma)$$-derivation $$d$$ of $$A$$ which approximates $$f$$. Camillo Trapani (Palermo)