Approximations of Set-Valued Functions by Metric Linear Operators

2005/06/06 by Nira Dyn, Dyn, Nira, Elza Farkhi +3
Mathematics · #26E25 #41A35 #41A36 #54C65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26E25 #msc:41A35 #msc:41A36 #msc:54C65

paper · pdf · doi:10.48550/arxiv.math/0506105

14 pages, 3 postscript figures

arxiv created 2005/06/06 · arxiv updated 2009/12/01

Abstract

In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new metric linear combinations of finite sequences of compact sets, thus obtaining "metric analogues" operators for set-valued functions. The new metric linear combination extends the binary metric average of Artstein. Approximation estimates for the metric analogue operators are derived. As examples we study metric Bernstein operators, metric Shoenberg operators and metric polynomial interpolants.

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