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Generalized set-valued variational inclusions and resolvent equations. (English) Zbl 1031.49016
Summary: In this paper, we establish the equivalence between generalized set-valued variational inclusions, resolvent equations, and the fixed-point problem, using the resolvent operator technique. This equivalence is used to suggest and analyze some iterative algorithms for solving generalized set-valued variational inclusions and related optimization problems.

MSC:
49J40Variational methods including variational inequalities
49J53Set-valued and variational analysis
47J20Inequalities involving nonlinear operators
47H04Set-valued operators
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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