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Special Topics in Majorization Theory
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 301-326Chapter in book (Refereed)
Abstract [en]

The primary aim of this chapter is to discuss the connection between the Hermite–Hadamard double inequality and Choquet’s theory. Noticed first by Niculescu (Math Inequal Appl 5(3):479–489, 2002, [356]), Niculescu (Math Inequal Appl 5(4):619–623, 2002, [357]) (during the conference Inequalities 2001, in Timişoara), this connection led him to a partial extension of the majorization theory beyond the classical case of probability measures, using the so-called Steffensen–Popoviciu measures. Their main feature is to offer a large framework under which the Jensen–Steffensen inequality remains available. As a consequence, one obtains the extension of the left-hand side of Hermite–Hadamard double inequality to a context involving signed Borel measures on arbitrary compact convex sets. A similar extension of the right-hand side of this inequality is known only in dimension 1, the higher dimensional case being still open.

Place, publisher, year, edition, pages
Cham: Springer, 2018. p. 301-326
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-69634DOI: 10.1007/978-3-319-78337-6_7ISBN: 978-3-319-78336-9 (print)ISBN: 978-3-319-78337-6 (electronic)OAI: oai:DiVA.org:ltu-69634DiVA, id: diva2:1220255
Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved

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Persson, Lars-Erik

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