Stability of $(α,β,γ)-$derivations on Lie $C^*-$algebras
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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 $(α,β,γ)-$derivations of Lie algebras. We say a functional equation $(ξ)$ is stable if any function $g$ satisfying the equation $(ξ)$ {\it approximately} is near to true solution of $(ξ).$ In the present paper, we investigate the stability of $(α,β,γ)-$derivations on Lie $C^*$-algebras associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3 x_3}{3})+ f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ }
10 pages
10 pages