Bull. Math. Soc. Sci. Math. Roumanie


Shoshana Abramovich, Graham Jameson and Gord Sinnamon:Refining Jensen's inequality, p.3-14
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Shoshana Abramovich, Graham Jameson and Gord Sinnamon: Refining Jensen's inequality, p. 3-14

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.

Key Words: Jensen's inequality, convex functions, concave functions, superadditive functions, subadditive functions .
2000 Mathematics Subject Classification: Primary: 26D15.