On extensions of kenderov's single-valuedness result for monotone maps and quasimonotone maps

D. Aussel, Y. García

Research output: Contribution to journalArticle in a journalpeer-review

2 Scopus citations

Abstract

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.
Original languageEnglish
Pages (from-to)702-713
Number of pages12
JournalSIAM Journal on Optimization
Volume24
Issue number2
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Lipschitz-like property
  • Monotone map
  • Quasi-monotone map
  • Single-directional property
  • Single-valuedness

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