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Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space. (English) Zbl 1142.47350
Summary: We introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain that the sequence converges strongly to a common element of two sets. Using this result, we prove three new strong convergence theorems in fixed point problems, variational inequalities and equilibrium problems.

##### MSC:
 47J05 Equations involving nonlinear operators (general) 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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##### References:
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