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Multivalued variational inequalities with \(D_J\)-pseudomonotone mappings in reflexive Banach spaces. (English) Zbl 1272.49018

Summary: This paper is concerned with the study of a class of variational inequalities with multivalued \(D_J\)-pseudomonotone mappings in reflexive Banach spaces by using the \(D_J\)-antiresolvent technique. An application to the multivalued nonlinear \(D_J\)-complementarity problem is also presented. The results coincide with the corresponding results announced by many others for the gradient state.

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
47H05 Monotone operators and generalizations
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