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

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.