 A subset formula_56 of formula_57 is said to be a monotone set if for every pair formula_58 and formula_59 in formula_56,

formula_56 is said to be maximal monotone if it is maximal among all monotone sets in the sense of set inclusion.The graph of a monotone operator formula_63 is a monotone set.A monotone operator is said to be maximal monotone if its graph is a maximal monotone set.