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Paatero’s Classes V(k) as Subsets of the Hornich Space

Paatero’s Classes V(k) as Subsets of the Hornich Space In this article we consider Paatero’s classes V(k) of functions of bounded boundary rotation as subsets of the Hornich space H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal H$$\end{document}. We show that for a fixed k≥2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k\ge 2$$\end{document} the set V(k) is a closed and convex subset of H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal H$$\end{document} and is not compact. We identify the extreme points of V(k) in H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal H$$\end{document}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Paatero’s Classes V(k) as Subsets of the Hornich Space

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-022-00472-2
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Abstract

In this article we consider Paatero’s classes V(k) of functions of bounded boundary rotation as subsets of the Hornich space H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal H$$\end{document}. We show that for a fixed k≥2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k\ge 2$$\end{document} the set V(k) is a closed and convex subset of H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal H$$\end{document} and is not compact. We identify the extreme points of V(k) in H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal H$$\end{document}.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Sep 20, 2022

Keywords: Paatero’s classes; Hornich spaces; Convex set; Extreme points; 30C45; 46B50

References

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    Brannan, DA; Clunie, JG; Kirwan, WE
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  • Untersuchungen über die Verzerrung bei konformen Abbildungen des Einheitskreises |z|<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|z| < 1$$\end{document}, die durch Funktionen mit nicht verschwindender Ableitung geliefert werden
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    Ponnusamy, S; Sahoo, SK; Sugawa, T