Let $A$ be a closed convex process from $R^n$ to $R^n$, $I$ be the identity map, $\lambda$ be a real number, and $k$ be a positive integer. It is obvious that $A - \lambda I$ is closed and so is $(A - \lambda I)^{-1}$ but I cannot find a way to prove that $(A - \lambda I)^{-k}$ is closed. I tried to use a condition found from Theorem 39.8 of Rockafellar's Convex Analysis:
Let $A$ and $B$ be convex processes from $R^n$ to $R^m$ and from $R^m$ to $R^p$, respectively. If $A$ and $B$ are closed and $\mathrm{ri}(\mathrm{range}B^*)$ meets $\mathrm{ri}(\mathrm{dom}A^*)$, then $BA$ is closed.
but couldn't make any progress. Would you give me any hint or a reference?