Metric approximation of set-valued functions of bounded variation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:349

Article; Proceedings Paper

Berdysheva, Elena E.¹  Dyn, Nira²  Farkhi, Elza²  Mokhov, Alona³ 

[1] Justus Liebig Univ Giessen, Giessen, Germany

[2] Tel Aviv Univ, Sch Math Sci, Tel Aviv, Israel

[3] Tel Aviv Acad Coll Engn, Afeka, Tel Aviv, Israel

关键词: Compact sets;    Set-valued functions;    Metric selections;    Metric linear combinations;    Metric integral;    Positive linear operators;   

DOI  :  10.1016/j.cam.2018.09.039

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free