Communications of the
Korean Mathematical Society CKMS

In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and G\u{a}vru\c{t}a stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-$\beta$-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.

Keywords: Multi-sextic mapping, Hyers--Ulam stability, fixed point method

MSC numbers: 39B52, 39B72, 39B82, 46B03