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Zbl 1167.47049
Moudafi, Abdellatif
Weak convergence theorems for nonexpansive mappings and equilibrium problems. (English)
[J] J. Nonlinear Convex Anal. 9, No. 1, 37-43 (2008). ISSN 1345-4773; ISSN 1880-5221/e

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 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49J40 Variational methods including variational inequalities
49M05 Methods of successive approximation based on necessary conditions
90C25 Convex programming

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

Cited in: Zbl 1167.47050

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