In this paper, we consider the solution mapping of equilibrium problems in a real Hilbert space, where the cost bifunction is convex forward to the second variable. By using the property that a point belongs to the solution set of the equilibrium problems if and only if it is a fixed point of the solution mapping, we obtain the contractiveness, nonexpansiveness and strictly pseudo-contractiveness of the solution mapping under some monotone assumptions of the bifunctions.

equilibrium problems, monotone, solution mapping, fixed point.