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Title: Approximation of Univariate Set-Valued Functions - an Overview
Authors: Dyn, Nira
Farkhi, Elza
Mokhov, Alona
Keywords: Compact Sets
Set-Valued Functions
Linear Approximation Operators
Minkowski Sum of Sets
Metric Average
Metric Linear Combinations
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 33, No 4, (2007), 495p-514p
Abstract: The paper is an updated survey of our work on the approximation of univariate set-valued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact convex images we use Minkowski convex combinations of sets, while for those with general compact images metric averages and metric linear combinations of sets are used. We obtain general approximation results and apply them to Bernstein polynomial operators, Schoenberg spline operators and polynomial interpolation operators.
Description: 2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.
ISSN: 1310-6600
Appears in Collections:Volume 33, Number 4

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