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A new iterative scheme with nonexpansive mappings for equilibrium problems. (English) Zbl 1273.65077

Summary: In this paper, we suggest a new iteration scheme for finding a common of the solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed points of a nonexpansive mapping. The scheme is based on both hybrid method and extragradient-type method. We obtain a strong convergence theorem for the sequences generated by these processes in a real Hilbert space. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature.

MSC:

65K10 Numerical optimization and variational techniques
65K15 Numerical methods for variational inequalities and related problems
90C25 Convex programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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