Stability of generalized mixed type additive-quadratic-cubic functional equation in non-Archimedean spaces

Abstract

In this paper, we prove generalized Hyres--Ulam--Rassias stability of the mixed type additive, quadratic and cubic functional equation $$f(x+ky)+f(x-ky)=k^{2}f(x+y)+k^{2}f(x-y)+2(1-k^2)f(x)$$ for fixed integers $k$ with $k\ne 0,\pm 1$ in non-Archimedean spaces.