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

Abstract

In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability of the following functional equation $$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+2(1-k^2)f(x)\eqno {2 cm}$$for fixed integers $k$ with $k\ne 0,\pm 1$ in the quasi-Banach spaces.