Abstract

We obtain the general solutions of the cubic functional equation 3[g(x+y)+g(xy)+6g(x)]=2g(2x+y)+2g(2xy)+g(xy)+g(x+y)+6g(x) and the Jensen-quadratic functional equation f((x+y)/2,z+w)+f((x+y)/2,zw)=f(x,z)+f(x,w)+f(y,z)+f(y,w).