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Maximal monotonicity of bifunctions

For each monotone bifunction F defined on a subset C of a Banach space, an associated monotone operator A F can be defined. The bifunction F is called maximal monotone, if A F is maximal monotone. We find conditions for a bifunction to be maximal monotone and show the relation to the existence of solutions of an equilibrium problem. Also, we establish some properties of the domain C when F is maximal monotone. Finally, we define and study cyclically monotone bifunctions.