One-Step iterative method for bilevel equilibrium problem in Hilbert space

The purpose of this paper is to introduce a simple iterative method for finding a solution of an equilibrium problem whose constraint is the solution set of another monotone equilibrium problem in a Hilbert space. Unlike the multi-step methods, the new method only requires to find one value of the proximal mapping associated with cost bifunctions at the current approximation over each iterative step. The strong convergence of the iterative sequence generated by the method is established by incorporating with a regularization technique. The numerical behavior of our method is also illustrated in comparison with several other methods.