Abstract
Some notions of generalized monotonicity for multi-valued mappings are characterized in terms of properties of the associated Minty variational inequalities. In particular, it is shown that the Minty variational inequality problem derived from a map F defined on a convex domain is solvable on any nonempty, compact, and convex subdomain if and only if F is properly quasimonotone.
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© 2001 Springer-Verlag Berlin Heidelberg
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John, R. (2001). A Note on Minty Variational Inequalities and Generalized Monotonicity. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_17
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DOI: https://doi.org/10.1007/978-3-642-56645-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41806-1
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