Separation by linear interpolation families

Mihály Bessenyei, Zsolt Páles

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

By standard separation theorems, if a convex function majorizes a concave one, then there exists an affine function between them. Moreover, a characterization of the existence of an affine separation between two arbitrary functions is also known. Motivated by these results, this note presents a necessary and sufficient condition for the existence of separation by members of a given linear interpolation family. The proof is based on the classical Helly theorem and reflects the geometric feature of the problem. In a particular case, the existence of a generalized convex (or concave) separation is also characterized.

Original languageEnglish
Pages (from-to)49-56
Number of pages8
JournalJournal of Nonlinear and Convex Analysis
Volume13
Issue number1
Publication statusPublished - Jan 1 2012

    Fingerprint

Keywords

  • Chebyshev systems
  • Convexity
  • Haar spaces
  • Helly's theorem
  • Separation theorems

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

Cite this