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

Moudafi, Abdellatif

J. Nonlinear Convex Anal. 9, No. 1, 37-43 (2008).

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

Keywords:

fixed point problem; variational inequality; inverse-strongly monotone operator; equilibrium problem; nonexpansive mapping