## Relaxed iterative algorithms for generalized mixed equilibrium problems with constraints of variational inequalities and variational inclusions.(English)Zbl 1472.47062

Summary: We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47J22 Variational and other types of inclusions 47H05 Monotone operators and generalizations 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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### References:

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