Resolvent of a monotone operator ($J_{\tau A}=(I+\tau A{)}^{-1}$)

For an operator $A$, its resolvent with step $\tau >0$ is $J_{\tau A}=(I+\tau A{)}^{-1}$. A maximal monotone operator has an everywhere-defined single-valued firmly nonexpansive mapping as its resolvent. For $A=\partial f$, the resolvent is the proximal map of $\tau f$. This monotone-operator resolvent uses a different convention from the spectral resolvent of a linear operator.