Solution and stability of generalized mixed type cubic, quadratic andadditive functional equation in quasi-Banach spaces

摘要

In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassiasstability of the following functional equation f (x + ky) + f (x — ky) = f (x + y) + k2 f (x — y) + 2(1 — k2)f (x) for fixed integers k with k 0, ±1 in the quasi-Banach spaces.