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In this article, we deal with stabilities of several functional equations in <i>n</i>-Banach spaces. For a surjective mapping <i>f</i> into a <i>n</i>-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic functional equation for <i>f</i> in <i>n</i>-Banach spaces.