Stability of $(\alpha,\beta,\gamma)-$derivations on Lie $C^*-$algebras
Abstract
Petr Novotný and Jiřĺ Hrivnák \cite{Nov} investigated generalize the concept of Lie derivations via certain complex parameters and obtained various Lie and Jordan operator algebras as well as two one- parametric sets of linear operators. Moreover, they established the structure and properties of $(\alpha,\beta,\gamma)-$derivations of Lie algebras. We say a functional equation $(\xi)$ is stable if any function $g$ satisfying the equation $(\xi)$ {\it approximately} is near to true solution of $(\xi).$ In the present paper, we investigate the stability of $(\alpha,\beta,\gamma)-$derivations on Lie $C^*$-algebras associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3 x_3}{3})+ f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ }
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2009
- DOI:
- 10.48550/arXiv.0905.2173
- arXiv:
- arXiv:0905.2173
- Bibcode:
- 2009arXiv0905.2173E
- Keywords:
-
- Mathematics - Differential Geometry;
- 17B05;
- 17B40;
- 46LXX
- E-Print:
- 10 pages