## Iterative algorithms for a new class of extended general nonconvex set-valued variational inequalities.(English)Zbl 1214.47065

Summary: Some new classes of extended general nonconvex set-valued variational inequalities and the extended general Wiener-Hopf inclusions are introduced. By the projection technique, the equivalence between the extended general nonconvex set-valued variational inequalities and fixed point problems as well as extended general nonconvex Wiener-Hopf inclusions is proved. Then, by using this equivalent formulation, we discuss the existence of solutions of the extended general nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of extended general nonconvex set-valued variational inequalities. We also verify that the approximate solutions obtained by our algorithms converge to the solutions of extended general nonconvex set-valued variational inequalities. The results presented in this paper extend and improve some known results from the literature.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H05 Monotone operators and generalizations 49J40 Variational inequalities 47J20 Variational and other types of inequalities involving nonlinear operators (general) 47J22 Variational and other types of inclusions
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