  The equilibrium problem defined by the Nikaid\^o-Isoda-Fan inequality
contains a number of problems such as optimization, variational inequality,
Kakutani fixed point, Nash equilibria, and others as special cases. This paper
presents a picture for the relationship between the fixed points of the Moreau
proximal mapping and the solutions of the equilibrium problem that satisfies
some kinds of monotonicity and Lipschitz-type condition.
