ให้ $x<y$
$\begin{array}{rcl}
h\left(\dfrac{x+y}{2}\right)&=&\dfrac{f\left(\dfrac{x+y}{2}\right)}{g\left(\dfrac{x+y}{2}\right)}\\
&&\\
&\leq&\dfrac{\dfrac{f(x)+f(y)}{2}}{\dfrac{g(x)+g(y)}{2}}\\
&&\\
&=&\dfrac{f(x)+f(y)}{g(x)+g(y)}\\
&&\\
&\leq&\dfrac{f(x)}{2g(x)}+\dfrac{f(y)}{2g(y)}\\
&&\\
&=&\dfrac{h(x)+h(y)}{2}
\end{array}$
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