Strong Quasi-nonexpansiveness of Solution Mappings of Equilibrium Problems

In this work we introduce a new approach for solving equilibrium problems in a real Hilbert space. First, we propose a solution mapping and show its strong quasi-nonexpansiveness. Next, we apply the mapping to present an algorithm for solving equilibrium problems. Strong convergence of the algorithm is showed under quasimonotone and Lipschitz-type continuous assumptions of the cost bifunctions. Finally, we give some numerical results for the proposed algorithm and comparison with some other known methods using the solution mapping.