Journal of the
Korean Mathematical Society JKMS

Our basic concern in this paper is to investigate some geometric properties of the graph of a maximal monotone operator in the one dimensional case. Using a well-known theorem of Minty, we answer S. Simons' questions affirmatively in the one dimensional case. Further developments of these results are also treated. In addition, we provide a new proof of Rockafellar's characterization of maximal monotone operators on $R$: every maximal monotone operator from $R$ to $2^R$ is the subdifferential of a proper convex lower semicontinuous function.

Keywords: maximal monotone operator, subdifferential of a convex function, cyclically monotone

MSC numbers: 47H05, 47H99