We prove the stability of the cubic functional equation f(2x + y) + f(2x− y) = 2f(x + y) + 2f(x− y) + 12f(x) in the setting of various spaces. AMS subject classifications: Primary 46S40, 39B82, 54E40

We establish some stability results concerning the general cubic functional equation f(x+ ky)− kf(x+ y) + kf(x− y)− f(x− ky) = 2k(k − 1)f(y) for fixed k ∈ N\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any ap...