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New iterative scheme with nonexpansive mappings for equilibrium problems and variational inequality problems in Hilbert spaces. (English) Zbl 1204.65082

The authors introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family of nonexpansive mappings in a Hilbert space and prove the strong convergence of the iterative scheme to the unique solution of a variational inequality problem. The authors propose that the iterative scheme of this paper can be studied in Banach spaces also.
In fact the paper will enter into the standard references in the field.

MSC:

65K15 Numerical methods for variational inequalities and related problems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49J40 Variational inequalities
65J15 Numerical solutions to equations with nonlinear operators
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References:

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