An additive $(u, \beta)$-functional equation and linear mappings in Banach modules
نویسندگان
1 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
2 Department of Mathematics, Hanyang University, Seoul 04763, Korea
3 Department of Data Science, Daejin University, Kyunggi 11159, Korea
doi
10.22075/ijnaa.2021.22580.2386چکیده
Let $A$ be a unital $C^*$-algebra. In this paper, we investigate the additive $(u, \beta)$-functional equation \begin{eqnarray}\label{0.1}f(x)+ u^* f(u y)+ f( z) = \beta^{-1} f(\beta(x+y+z))\end{eqnarray}for all unitary elements $u$ in $A$ and for a fixed nonzero complex number $\beta$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive $(u, \beta)$-functional equation (\ref{0.1}) in Banach modules.
