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Exceptional families of elements for variational inequalities in Banach spaces. (English) Zbl 1136.49007
Summary: In keeping with very recent efforts to establish a useful concept of an exceptional family of elements for variational inequality problems rather than complementarity problems as in the past, we propose such a concept. It generalizes previous ones to multivalued variational inequalities in general normed spaces and allows us to obtain several existence results for variational inequalities corresponding to earlier ones for complementarity problems. Compared with the existing literature, we consider problems in more general spaces and under considerably weaker assumptions on the defining map.
MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
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