On extensions of Kenderov’s single-valuedness result for monotone maps

Abstract:

One of the most famous single-valuedness results for set-valued maps is due to Kenderov and states that a monotone set-valued operator is single-valued at any point where it is lower semi-continuous. This has been extended in Christensen-Kenderov to monotone maps satisfying a so-called property. Our aim in this work is twofold: First, to prove that the property assumption can be weakened; second to emphasize that these classical single-valuedness results for monotone operators can be obtained, in very simple way, as direct consequences of counterpart results proved for quasimonotone operators in terms of single-directionality

Posted on Nov 11, 2013 in Optimization and Equilibrium, Seminars