The resolvent order: a unification of the orders by Zarantonello, by   Loewner, and by Moreau
  We introduce and investigate the resolvent order, which is a binary relation on the set of firmly nonexpansive mappings. It unifies well-known orders introduced by Loewner (for positive semidefinite matrices) and by Zarantonello (for projectors onto convex cones). A connection with Moreau's order of convex functions is also presented. We also construct partial orders on (quotient sets of) proximal mappings and convex functions. Various examples illustrate our results. 
Sedi Bartz, Heinz H. Bauschke and Xianfu Wang
math.FA math.OC