Two multi-cubic functional equations and some results on the stability in modular spaces

Abstract

In this article, we study n-variable mappings which are cubic in each variable. We also show that such mappings can be described by an equation, say, multi-cubic functional equation. Furthermore, we study the stability of such functional equations in the modular space X rho by applying Delta 2-condition and the Fatou property (in some cases) on the modular function rho. Finally, we show that, under some mild conditions, one of these new multi-cubic functional equations can be hyperstable.