The Metric Integral of Set-Valued Functions View Full Text


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Article Info

DATE

2017-03-23

AUTHORS

Nira Dyn, Elza Farkhi, Alona Mokhov

ABSTRACT

This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in ℝd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb {R}}^d$\end{document}. The new integral, termed the metric integral, is defined using metric linear combinations of sets and is shown to consist of integrals of all the metric selections of the integrated multifunction. The metric integral is a subset of the Aumann integral, but in contrast to the latter, it is not necessarily convex. For a special class of segment functions equality of the two integrals is shown. Properties of the metric selections and related properties of the metric integral are studied. Several indicative examples are presented. More... »

PAGES

867-885

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11228-017-0403-1

DOI

http://dx.doi.org/10.1007/s11228-017-0403-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1084030396


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