TY - JOUR
T1 - Metric approximation of set-valued functions of bounded variation
AU - Berdysheva, Elena E.
AU - Dyn, Nira
AU - Farkhi, Elza
AU - Mokhov, Alona
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - 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.
AB - 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.
KW - Compact sets
KW - Metric integral
KW - Metric linear combinations
KW - Metric selections
KW - Positive linear operators
KW - Set-valued functions
UR - http://www.scopus.com/inward/record.url?scp=85054802758&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2018.09.039
DO - 10.1016/j.cam.2018.09.039
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AN - SCOPUS:85054802758
SN - 0377-0427
VL - 349
SP - 251
EP - 264
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -