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In this note prove the following Berwald-type inequality, showing that forany integrable log-concave function $f:\mathbb R^n\rightarrow[0,\infty)$ andany concave function $h:L\rightarrow\mathbb [0,\infty)$, where $L$ is theepigraph of $-\log \frac{f}{\Vert f\Vert_\infty}$, then  $$p\to  \left(\frac{1}{\Gamma(1+p)\int_L e^{-t}dtdx}\int_Lh^p(x,t)e^{-t}dtdx\right)^\frac{1}{p}  $$ is decreasing in $p\in(-1,\infty)$, extending the range of $p$ where themonotonicity is known to hold true.  As an application of this extension, we will provide a new proof of afunctional form of Zhang's reverse Petty projection inequality, recentlyobtained in [ABG].

An extension of Berwald's inequality and its relation to Zhang's inequality