Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2573

 Title: Approximation of Univariate Set-Valued Functions - an Overview Authors: Dyn, NiraFarkhi, ElzaMokhov, Alona Keywords: Compact SetsSet-Valued FunctionsLinear Approximation OperatorsMinkowski Sum of SetsMetric AverageMetric 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. URI: http://hdl.handle.net/10525/2573 ISSN: 1310-6600 Appears in Collections: Volume 33, Number 4

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