An extragradient-type algorithm for solving a nonmonotone equilibrium problem over the fixed point set in a Hilbert space

We present an extragradient-type algorithm for solving a nonmonotone and non-Lipschitzian equilibrium problem over the fixed point set of a nonexpansive mapping in a Hilbert space. We obtain that the sequence generated by the presented algorithm converges weakly to a solution of the problem. The weak convergence does not require any monotonicity and Lipschitz continuity of the involved equilibrium function. This is a result of projecting the current point onto shrinking convex subsets of the feasible set at each iteration and employing an Armijo-type linesearch with subgradient. The numerical behavior has shown the efficiency of the proposed algorithm.