On the proximal point method for equilibrium problems in Hilbert spaces

We analyse a proximal point method for equilibrium problems in Hilbert spaces, improving upon previously known convergence results. We prove global weak convergence of the generated sequence to a solution of the problem, assuming existence of solutions and rather mild monotonicity properties of the bifunction which defines the equilibrium problem, and we establish existence of solutions of the proximal subproblems. We also present a new reformulation of equilibrium problems as variational inequalities ones.