We discuss monotone properties of Furuta type inequalities: 
Let $A \ge B \ge 0$ and $0 \le t \le p$. 
Then for each $t \in [0,\ 1],\ A^t\ \sharp_{\frac{1-t}{p-t}}\ B^p$ is 
increasing for $p \ge 1$, and if $A^p \ge B^p$ for some fixed $p > 0$, 
then $A^t\ \sharp_{\frac{1-t}{p-t}}\ B^p$ is increasing for $t \in [0,1]$. 
Moreover, if $A^t \ge B^t$ for some fixed $t > 0$, 
then the following inequalities hold;\\
$$for\ \ t \le \beta \le p,\ \ 
(A^t\ \natural_{\frac{\beta-t}{p-t}}\ B^p)^{\frac{\delta}{\beta}} 
\le B^{\delta} \le A^t\ \sharp_{\frac{\delta-t}{p-t}}\ B^p,$$
$$for\ \ p \le \delta \le \beta,\ \ 
(A^t\ \natural_{\frac{\beta-t}{p-t}}\ B^p)^{\frac{\delta}{\beta}} 
\le A^t\ \natural_{\frac{\delta-t}{p-t}}\ B^p.$$
Consequently, it improves a recent result of Yang and Zuo.