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Set-valued resolvent equations and mixed variational inequalities. (English) Zbl 1021.49002
Summary: In this paper, we introduce and study a new class of variational inequalities, which are called the generalized set-valued mixed variational inequalities. The resolvent operator technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed-point problems, and the generalized set-valued resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems.

MSC:
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces