Hyperstability results for a generalized radical cubic functional equation related to additive mapping in non-Archimedean Banach spaces

The aim of this paper is to introduce and solve the following generalized radical cubic functional equation $$\begin{aligned} f\left( \root 3 \of {\sum _{i=1}^{k}x_{i}^{3}}\right) =\sum _{i=1}^{k}f(x_{i}),\quad k\in \mathbb {N}_{2}. \end{aligned}$$ We also investigate some hyperstability results for this equation in non-Archimedean Banach spaces.