Solution and stability of generalized mixed type additive and quadratic functional equation in non-Archimedean spaces

Abstract

In this paper, we achieve the general solution and the generalized Hyres–Ulam–Rassias stability of the following additive–quadratic functional equation $$f (x + ky) + f (x - ky) = f (x + y) + f (x - y) + \frac{2(k + 1)}{k} f (ky) - 2(k + 1)f (y)$$ for fixed integers k with k ≠ 0, ±1 in non-Archimedean spaces.