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...

In this paper, we investigate a fuzzy version of stability for the functional equation f(x+ 2y)− 2f(x+ y) + 2f(x− y)− f(x− 2y)− f(2y) + 4f(−y) = 0 in the sense of Mirmostafaee and Moslehian. Mathematics Subject Classification: 39B82, 39B52

We study the generalized Hyers-Ulam stability of the functional equation f[x1,x2,x3]= h(x1+x2+x3). 2000 Mathematics Subject Classification. 39B22, 39B82.

We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2(k − k)f(x) for all k ∈ N and the quartic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2k(k − 1)f(x)− 2(k − 1)f(y) for all k ∈ N in non-Archimedean normed spaces.