 ${\ensuremath{\varphi}}$-uniformly firmly nonexpansive.  Fact \[resolvents of subs and proximal reformulation\] guarantees that ${\ensuremath{\varphi}}=p_{\frac{0}{0}}(\boldsymbol{{\ensuremath{\varphi}}},\boldsymbol{\lambda})$ is lower semicontinuous, convex and that for every $