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.


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