Two multi-cubic functional equations and some results on the stability in modular spaces
Choonkil Park, Abasalt Bodaghi
Abstract
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 $X_{\rho }$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>X</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:math> by applying $\Delta _{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Δ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> -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.