Approximations of Set-Valued Functions by Metric Linear Operators

@inproceedings{Dyn2005ApproximationsOS,
title={Approximations of Set-Valued Functions by Metric Linear Operators},
author={Nira Dyn and Elza Farkhi and Alona Mokhov},
year={2005}
}

In this work, we introduce new approximation operators for univariate setvalued 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… CONTINUE READING