For maximally monotone linear relations, dense type, negative-infimum   type, and Fitzpatrick-Phelps type all coincide with monotonicity of the   adjoint
  It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick-Phelps type are the same and equivalent to monotonicity of the adjoint. This result also provides affirmative answers to two problems: one posed by Phelps and Simons, and the other by Simons. 
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang and Liangjin Yao
math.FA