Eigenfunction of an absolutely one-homogeneous functional ($\lambda f\in \partial J(f)$)

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.