Refining Jensen's inequality

Refining Jensen's inequality

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 s...

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Veröffentlicht in:Bulletin mathématiques de la Société des sciences mathématiques de Roumanie 2004-01, Vol.47 (95) (1/2), p.3-14
Hauptverfasser: Abramovich, Shoshana, Jameson, Graham, Sinnamon, Gord
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Convexity
Industrial refining
Integrands
Mathematical functions
Mathematical inequalities
Mathematical theorems
Tangents
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Zusammenfassung: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 from [3]. The refined Jensen's inequality is used to prove a Minkowski inequality with upper and lower estimates.
ISSN:1220-3874
2065-0264