TY - JOUR
T1 - On extensions of kenderov's single-valuedness result for monotone maps and quasimonotone maps
AU - Aussel, D.
AU - García, Y.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - One of the most famous single-valuedness results for set-valued maps is due to Kenderov [Fund. Math., LXXXVIII (1975), pp. 61-69] and states that a monotone set-valued operator is single-valued at any point where it is lower semicontinuous. This has been extended in Christensen and Kenderov [Math. Scand., 54 (1984), pp. 70-78] 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, and 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 quasi-monotone operators in terms of single-directionality.
AB - One of the most famous single-valuedness results for set-valued maps is due to Kenderov [Fund. Math., LXXXVIII (1975), pp. 61-69] and states that a monotone set-valued operator is single-valued at any point where it is lower semicontinuous. This has been extended in Christensen and Kenderov [Math. Scand., 54 (1984), pp. 70-78] 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, and 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 quasi-monotone operators in terms of single-directionality.
KW - Lipschitz-like property
KW - Monotone map
KW - Quasi-monotone map
KW - Single-directional property
KW - Single-valuedness
KW - Lipschitz-like property
KW - Monotone map
KW - Quasi-monotone map
KW - Single-directional property
KW - Single-valuedness
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U2 - 10.1137/120880215
DO - 10.1137/120880215
M3 - Article in a journal
SN - 1052-6234
VL - 24
SP - 702
EP - 713
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 2
ER -