TY - JOUR
T1 - Refining Jensen's inequality
AU - Abramovich, Shoshana
AU - Jameson, Graham
AU - Sinnamon, Gord
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
UR - https://www.jstor.org/stable/43678937
M3 - Article
SN - 1220-3874
VL - 47
SP - 3
EP - 14
JO - Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
JF - Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
IS - 95
ER -