Order isomorphisms in windows

Research output: Contribution to journalArticlepeer-review

Abstract

We characterize order preserving transforms on the class of lowersemi- continuous convex functions that are defined on a convex subset of Rn (a "window") and some of its variants. To this end, we investigate convexity preserving maps on subsets of ℝn. We prove that, in general, an order isomorphism is induced by a special convexity preserving point map on the epi-graph of the function. In the case of non-negative convex functions on K, where 0 Ie{cyrillic, ukrainian} K and f(0) = 0, one may naturally partition the set of order isomorphisms into two classes; we explain the main ideas behind these results.

Original languageEnglish
Pages (from-to)112-118
Number of pages7
JournalElectronic Research Announcements in Mathematical Sciences
Volume18
DOIs
StatePublished - 2011

Keywords

  • Convex functions
  • Fractional linear maps
  • Order isomorphisms

All Science Journal Classification (ASJC) codes

  • General Mathematics

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