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In this paper, we establish the general solution of the functional equation$$f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0cm}$$for fixed integers $n$ with $n\neq0,\pm1$ and investigate the generalizedHyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

On the stability of generalized mixed type quadratic and quartic functional equation in quasi-Banach spaces