Absolutely one-homogeneous functional

A functional $J$ is absolutely one-homogeneous when $J(cu)=|c|J(u)$ for every scalar $c$. For a convex such functional,

A nonzero vector $f$ is an eigenfunction of an absolutely one-homogeneous convex functional $J$ with eigenvalue $\lambda$ when $\lambda f\in \partial J(f)$. This nonlinear analogue of an eigenvector underlies exact shrinkage formulas for several variational flows and proximal maps.