Stability Mixed Quadratic Equation -Cauchy Function

In this paper,we establish the general solution of the Mixed quadratic-Cauchy functi-on equation f(x1+2x2,y1)+f(x1-2x2,y1)+f(x1+2x2,y2)+f(x1-2x2,y2)+8f(x2,y1)+8f(x2,y2)=2f(x1,y1+y2+4f(2x2,y1+y2) and the stability of this equation shall be investigated.In the first two chapters of this paper,first give the definition and general solution of the Mixed quadratic-Cauchy function equation,then prove its stability in Barach space.In the third chapter,furthermore,the stability of this equation shall also be treated under non-Archimedean space.