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Find all function $f,g$ that satisfy: $$g(x)-g(y)=\frac{1}{6} (x-y)(f(x)+f((x+y)/2)+f(y))$$ For $y=0$ we have an equation in $f$: $$4(x-y)(f(x/2)-f(x/2+y/2))=xf(y)-yf(x)$$ How can i do it?

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    Could you kindly typeset your question to make it more readable? http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference2012-11-22
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    Why does $y$ appear in the equation with $y=0$ and why does $g$ not appear?2012-11-22

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