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

[摘要] 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 ρ. Finally, we show that, under some mild conditions, one of these new multi-cubic functional equations can be hyperstable.

[学科分类] 电力

[关键词] Modular space;(Multi)-cubic functional equation;Hyers–Ulam stability