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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.

47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
47J22Variational and other types of inclusions
Full Text: DOI
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