Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces

We prove generalized Hyers-Ulam-Rassias stability of the cubic functional equation f (kx+ y)+ f (kx-y) = k[f (x+ y)+ f (x-y)]+ 2(k(3)-k) f (x) for all k. N and the quartic functional equation f (kx + y)+ f (kx-y) = k(2)[f (x + y)+ f (x-y)]+ 2k(2)(k(2)-1) f (x)-2(k(2)-1) f (y) for all k is an element of N in non-Archimedean normed spaces.