Nonlinear Sherman-type inequalities
Abstract: An important class of Schur-convex functions is generated by convex functions via the well-known Hardy–Littlewood–Pólya–Karamata inequality. Sherman’s inequality is a natural generalization of the HLPK inequality. It can be viewed as a comparison of two special inner product expressions induced by a convex function of one variable. In the present note, we extend the Sherman inequality from the (bilinear) inner product to a (nonlinear) map of two vectorial variables satisfying the Leon–Proschan condition. Some applications are shown for directional derivatives and gradients of Schur-convex functions.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Nonlinear Sherman-type inequalities ; volume:9 ; number:1 ; year:2018 ; pages:168-175 ; extent:8
Advances in nonlinear analysis ; 9, Heft 1 (2018), 168-175 (gesamt 8)
- Creator
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Niezgoda, Marek
- DOI
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10.1515/anona-2018-0098
- URN
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urn:nbn:de:101:1-2405021556368.324971577081
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:48 AM CEST
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Associated
- Niezgoda, Marek
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