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Quasimonotone variational inequalities in Banach spaces

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Abstract

Various existence results for variational inequalities in Banach spaces are derived, extending some recent results by Cottle and Yao. Generalized monotonicity as well as continuity assumptions on the operatorf are weakened and, in some results, the regularity assumptions on the domain off are relaxed significantly. The concept of inner point for subsets of Banach spaces proves to be useful.

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This work was completed while the first author was visiting the Graduate School of Management of the University of California, Riverside. The author wishes to thank the School for its hospitality.

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Hadjisavvas, N., Schaible, S. Quasimonotone variational inequalities in Banach spaces. J Optim Theory Appl 90, 95–111 (1996). https://doi.org/10.1007/BF02192248

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