Approximations of Set-Valued Functions by Metric Linear Operators

Details Approximations of Set-Valued Functions by Metric Linear Operators Approximations of Set-Valued Functions by Metric Linear Operators

2005-06-06

arxiv.org/abs/math/0506105v1

Mathematics

Classical Analysis and ODEs

14 pages, 3 postscript figures

Scientific paper

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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