李$C^*-$代数上$(α,β,γ)-$导子的稳定性
Stability of $(α,β,γ)-$derivations on Lie $C^*-$algebras
摘要：
Petr Novotnovich和JienkiHrivnák \cite{Nov}研究推广了含复参数的Lie导子的概念，得到了各种Lie和Jordan算子代数以及两个单参数线性算子集.建立了李代数的$(α,β,γ)-$导子的结构和性质。我们称一个函数方程$(ξ)$是稳定的，如果满足方程$(ξ)$ { \it近似}的函数$g$接近于$(ξ).$的真解。本文研究了李$C^*$ -代数上与下列函数方程$$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3 x_3}{3})+ f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ }相关的$(α,β,γ)-$导子的稳定性
英文摘要：
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 $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3 x_3}{3})+ f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ }
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
