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Iterative algorithms for general multivalued variational inequalities. (English) Zbl 1232.49012
Summary: We introduce and study some new classes of variational inequalities and the Wiener-Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and analyze some iterative methods for solving the general multivalued variational in equalities in conjunction with nonexpansive mappings. We prove a strong convergence result for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general multivalued variational inequalities under some mild conditions. Several special cases are also discussed.
MSC:
49J40Variational methods including variational inequalities
49M30Other numerical methods in calculus of variations
49J21Optimal control problems involving relations other than differential equations
47H09Mappings defined by “shrinking” properties