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Existence of solutions and $\alpha$-well-posedness for a system of constrained set-valued variational inequalities

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  • The notions of $\alpha$-well-posedness and generalized $\alpha$-well-posedness for a system of constrained variational inequalities involving set-valued mappings (for short, (SCVI)) are introduced in Hilbert spaces. Existence theorems of solutions for (SCVI) are established by using penalty techniques. Metric characterizations of $\alpha$-well-posedness and generalized $\alpha$-well-posedness, in terms of the approximate solutions sets, are presented. Finally, the equivalences between (generalized) $\alpha$-well-posedness for (SCVI) and existence and uniqueness of its solutions are also derived under quite mild assumptions.
    Mathematics Subject Classification: Primary: 47J04, 49K40; Secondary: 90C31.

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