Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

摘要

In this paper we establish the general solution of the functional equation $$f(x + 2y) + f(x - 2y) + 4f(x) = 3[f(x + y) + f(x - y)] + f(2y) - 2f(y)$$ and investigate the Hyers–Ulam–Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers–Ulam–Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.