On the stability of a quadratic functional equation over non-Archimedean spaces

Abstract

Let G be an abelian group and suppose that X is a non-Archimedean Banach space. We study Hyers-Ulam-Rassias stability for the functional equation of quadratic type $$f (x + y + z) + f (x) + f (y) + f (z) = f (x + y) + f (y + z) + f (z + x)$$ where $f : G\to X$ is a map.