Convex KKM maps, monotone operators and Minty variational inequalities

Marc Lassonde

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arXiv · 1503.06363

Convex KKM maps, monotone operators and Minty variational inequalities

Marc Lassonde

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Abstract

It is known that for convex sets, the KKM condition is equivalent to the finite intersection property. We use this equivalence to obtain a characterisation of monotone operators in terms of convex KKM maps and in terms of the existence of solutions to Minty variational inequalities. The latter result provides a converse to the seminal theorem of Minty.

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Marc Lassonde. 2015-03-21. Convex KKM maps, monotone operators and Minty variational inequalities. https://arxiv.org/abs/1503.06363

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