$P$-convexity of Musielak-Orlicz sequence spaces of Bochner type

It is proved that the Musielak-Orlicz sequence space $l_\varphi(X)$ of Bochner type is $\texttt{P}$-convex if and only if both spaces $l_\varphi(\mathbb{R})$ and $X$ are $\texttt{P}$-convex. In particular, the Lebesgue-Bochner sequence space $l^p(X)$ is $\texttt{P}$-convex if $X$ is $\texttt{P}$-convex and $1 < p <\infty$.