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Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems. (English) Zbl 1110.49013
Summary: We introduce an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. The iterative process is based on so-called extragradient method. We obtain a strong convergence theorem for two sequences generated by this process.

MSC:
 49J40 Variational inequalities 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47J20 Variational and other types of inequalities involving nonlinear operators (general)
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