  Monotone operators are of central importance in modern optimization and
nonlinear analysis. Their study has been revolutionized lately, due to the
systematic use of the Fitzpatrick function. Pioneered by Penot and Svaiter, a
topic of recent interest has been the representation of maximal monotone
operators by so-called autoconjugate functions. Two explicit constructions were
proposed, the first by Penot and Zalinescu in 2005, and another by Bauschke and
Wang in 2007. The former requires a mild constraint qualification while the
latter is based on the proximal average.
  We show that these two autoconjugate representers must coincide for
continuous linear monotone operators on reflexive spaces. The continuity and
the linearity assumption are both essential as examples of discontinuous linear
operators and of subdifferential operators illustrate. Furthermore, we also
construct an infinite family of autoconjugate representers for the identity
operator on the real line.
