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It is shown that, for maximally monotone linear relations defined on ageneral Banach space, the monotonicities of dense type, of negative-infimumtype, and of Fitzpatrick-Phelps type are the same and equivalent tomonotonicity of the adjoint. This result also provides affirmative answers totwo problems: one posed by Phelps and Simons, and the other by Simons.

For maximally monotone linear relations, dense type, negative-infimum  type, and Fitzpatrick-Phelps type all coincide with monotonicity of the  adjoint