ITERATIVE ALGORITHMS FOR SOLVING MIXED EQUILIBRIUM PROBLEMS AND CONSTRAINED CONVEX MINIMIZATION PROBLEMS

In this paper, we introduce new implicit and explicit iterative algorithms for finding a common element of the set of solutions of a mixed equilibrium problem and the set of solutions of a constrained convex minimization problem in Hilbert spaces. Under suitable control conditions, we prove that the sequences generated by the proposed algorithms converge strongly to a common element of two sets, which is the unique solution of a certain variational inequality.