Every maximally monotone operator of Fitzpatrick-Phelps type is actually   of dense type
  We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide. 
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang and Liangjin Yao
math.FA