Stability of cubic and quartic functional equations in non-Archimedean spaces

M. Eshaghi Gordji; M. Bavand Savadkouhi

paper

Stability of cubic and quartic functional equations in non-Archimedean spaces

arXiv:0812.5015

Abstract

We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation $f (k x + y) + f (k x - y) = k [f (x + y) + f (x - y)] + 2 (k^{3} - k) f (x)$ for all $k \in N$ and the quartic functional equation $f (k x + y) + f (k x - y) = k^{2} [f (x + y) + f (x - y)] + 2 k^{2} (k^{2} - 1) f (x) - 2 (k^{2} - 1) f (y)$ for all $k \in N$ in non-Archimedean normed spaces.