Abstract

We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.
Lingua originaleEnglish
pagine (da-a)421-430
Numero di pagine10
RivistaJournal of Optimization Theory and Applications
Volume187
DOI
Stato di pubblicazionePubblicato - 2020

Keywords

  • Convex set
  • Extension
  • Normed linear space
  • Quasiconvex function

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