Projection algorithms for solving nonmonotone equilibrium problems in Hilbert space

We propose two projection algorithms for solving an equilibrium problem where the bifunction is not required to be satisfied any monotone property. Under assumptions on the continuity, convexity of the bifunction and the nonemptyness of the solution set of the Minty equilibrium problem, we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the primal equilibrium problem respectively. © 2016 Elsevier B.V. All rights reserved.