Wednesday, March 16, 2016

Cauchy functional equation three variables

If I have function from R3 to R satisfying



f(x1,x2,x3)+f(y1,y2,y3)=f(x1+y1,x1+y2,x3+y3)


is it necessarily linear?


f(z1,z2,z3)=λ1z1+λ2z2+λ3z3


Wasn't sure if this was a direct consequence of Cauchy's theorem or not.

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