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Refining Jensen's inequality.

Research output: Contribution to journalJournal article


Journal publication date1/12/2004
JournalBulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Volume47 (95
Number of pages12
Original languageEnglish


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.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics