Refined functional equations stemming from cubic, quadratic and additive mappings (Q1044332)

Refining the works of \textit{K. Jun} and \textit{H. Kim} [J. Math. Anal. Appl. 274, No.~2, 867--878 (2002; Zbl 1021.39014) and Bull. Belg. Math. Soc. - Simon Stevin 13, No.~2, 271--285 (2006; Zbl 1132.39022)], the authors consider the functional equation \[ \begin{multlined} f\left(\sum_{j=1}^{n-1} x_j+2x_n\right)+f\left(\sum_{j=1}^{n-1}x_j-2x_n\right)+8\sum_{j=1}^{n-1} f(x_j)\\ =2f\left(\sum_{j=1}^{n-1}x_j\right)+4\sum_{j=1}^{n-1}[f(x_j+x_n)+f(x_j-x_n)]~~~~(n\geq 2)\end{multlined} \] containing as solutions cubic, quadratic and additive mappings. They investigate the Hyers-Ulam stability of this equation in the setting of Banach spaces.