Abstract: In this paper, we present a new method for solving equilibrium problem over the fixed point set of a firmly nonexpansive mapping, where the underlying bifunction is continuous but not necessarily monotone. Firstly, we construct a closed ball by introducing some parameters. Then, we calculate the intermediate iterate by the projection of the inexact subgradient onto the closed convex set. The next iterate is obtained as the firmly nonexpansive mapping of a convex combination, which consists of the current iterate and the intermediate iterate. Finally, we analyse the convergence properties and the global convergence of the algorithm under some suitable conditions.

Key words: equilibrium problem, firmly nonexpansive mapping, inexact subgradient algorithm global convergence