## Weak convergence theorems for nonexpansive mappings and equilibrium problems.(English)Zbl 1167.47049

Summary: We introduce a convergent method for approximating a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a monotone equilibrium problem. Using the main convergence theorem we obtain results which improve, develop and unify several results in fixed point problems, variational inequalities and equilibrium problems.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 49J40 Variational inequalities 49M05 Numerical methods based on necessary conditions 90C25 Convex programming