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I have a function $f(x,y)$ defining on $x>0,y>0$ satisfying that

(1) $f>0$

(2) for $a>1, f(ax,ay)>af(x,y)$

(3) $f_x,f_y>0$


Can I say something about $f_{xy}$, particularly, if $f_{xy}>0$?

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