Additive functional equation; Quadratic functional equation; Non-Archimedean space Stability
Issue Date
2012-05
Publisher
SPRINGER
Citation
ANNALI DELL'UNIVERSITA' DI FERRARA, Vol.58, No.1 [2012], p49–64
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.