 guarantees that $J_{{\ensuremath{\mathcal{R}({\bf A},{\boldsymbol \lambda})}}}=\sum_{i\in I}\lambda_i J_{A_i}$ is firmly nonexpansive with modulus ${\ensuremath{\varphi}}=p_{\frac{0}{0}}(\boldsymbol{{\ensuremath{\varphi}}},\boldsymbol{\lambda})$, which, in turn, implies that ${\ensuremath{\mathcal{R}({\bf A},{\boldsymbol \lambda})}}$ is monotone with modulus ${\ensuremath{\varphi}}$. 