Conference paper

Metric approximation of set-valued functions of bounded variation


Authors listBerdysheva, Elena E.; Dyn, Nira; Farkhi, Elza; Mokhov, Alona

Publication year2019

Pages251-264

JournalJournal of Computational and Applied Mathematics

Volume number349

ISSN0377-0427

eISSN1879-1778

Open access statusBronze

DOI Linkhttps://doi.org/10.1016/j.cam.2018.09.039

Conference2nd Conference on Subdivision, Geometric and Algebraic Methods, Isogeometric Analysis and Refinability in Italy (SMART)

PublisherElsevier


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. (C) 2018 Elsevier B.V. All rights reserved.



Citation Styles

Harvard Citation styleBerdysheva, E., Dyn, N., Farkhi, E. and Mokhov, A. (2019) Metric approximation of set-valued functions of bounded variation, Journal of Computational and Applied Mathematics, 349, pp. 251-264. https://doi.org/10.1016/j.cam.2018.09.039

APA Citation styleBerdysheva, E., Dyn, N., Farkhi, E., & Mokhov, A. (2019). Metric approximation of set-valued functions of bounded variation. Journal of Computational and Applied Mathematics. 349, 251-264. https://doi.org/10.1016/j.cam.2018.09.039


Last updated on 2025-10-06 at 10:57