Metric approximation of set-valued functions of bounded variation

Elena E. Berdysheva, Nira Dyn, Elza Farkhi, Alona Mokhov

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we approximate univariate set-valued functions (SVFs) of bounded variation with range consisting of general (not necessarily convex) compact sets. The approximation operators adapted to SVFs are local operators such as the symmetric Schoenberg spline operator, the Bernstein polynomial operator and the Steklov function. All operators are adapted by using metric linear combinations. Error bounds, obtained in the averaged Hausdorff metric, provide rates of approximation similar to those for real-valued functions of bounded variation.

Original languageEnglish
Pages (from-to)251-264
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume349
DOIs
StatePublished - 15 Mar 2019

Keywords

  • Compact sets
  • Metric integral
  • Metric linear combinations
  • Metric selections
  • Positive linear operators
  • Set-valued functions

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