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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
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