  The correspondence between the monotonicity of a (possibly) set-valued
operator and the firm nonexpansiveness of its resolvent is a key ingredient in
the convergence analysis of many optimization algorithms. Firmly nonexpansive
operators form a proper subclass of the more general - but still pleasant from
an algorithmic perspective - class of averaged operators. In this paper, we
introduce the new notion of conically nonexpansive operators which generalize
nonexpansive mappings. We characterize averaged operators as being resolvents
of comonotone operators under appropriate scaling. As a consequence, we
characterize the proximal point mappings associated with hypoconvex functions
as cocoercive operators, or equivalently; as displacement mappings of conically
nonexpansive operators. Several examples illustrate our analysis and
demonstrate tightness of our results.
