 Cocoercivity

An operator $G$ is $\beta$-cocoercive when $⟨Gz-Gw,z-w⟩\ge \beta \Vert Gz-Gw{\Vert }^2$ with $\beta >0$. This strengthens monotonicity and implies a Lipschitz constant $1/\beta$ by the Cauchy-Schwarz inequality. Gradient maps of smooth convex functions provide an important converse through the Baillon–Haddad theorem.