Alona Mokhov

Approximation of set-valued functions : adaptation of classical approximation operators

Scientific Background: On Functions with Values in Metric Spaces: Basic Notions, Approximation Operators On Sets: Sets, Set Operations and Parametrizations On Set-Valued Functions (SVFs): Representations and Regularity Approximation of SVFs: Methods Based on Canonical Representations Methods Based on Minkowski Convex Combinations Methods Based on the Metric Average Methods Based on Metric Linear Combinations Methods Based on Metric Selections Approximation of SVFs with Images in R: Regularity of the Boundaries of the Graph Multisegmental and Topological Representations Methods Based on Topological Representation.

Metric approximation of set-valued functions of bounded variation

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.