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Refining Jensen's inequality.

Jameson, Graham J. O. and Abramovich, Shoshana and Sinnamon, Gord (2004) Refining Jensen's inequality. Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 47 (95 (1-2). pp. 3-14. ISSN 1220-3874

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Abstract

A refinement of Jensen's inequality is presented. An extra term makes the inequality tighter when the convex function is ``superquadratic," a strong convexity-type condition introduced here. This condition is shown to be necessary and sufficient for the refined inequality. It is also shown to be strictly intermediate between two points of the scale of convexity. The refined Jensen's inequality is used to prove a Minkowski inequality with upper and lower estimates.

Item Type: Article
Journal or Publication Title: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Additional Information: RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
Uncontrolled Keywords: Jensen's inequality ; convex functions ; concave functions ; superadditive functions ; subadditive functions .
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 2373
Deposited By: ep_importer
Deposited On: 01 Apr 2008 16:28
Refereed?: Yes
Published?: Published
Last Modified: 14 Oct 2013 12:55
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/2373

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