Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Refining Jensen's inequality.
AU - Jameson, Graham J. O.
AU - Abramovich, Shoshana
AU - Sinnamon, Gord
N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
PY - 2004/12/1
Y1 - 2004/12/1
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. 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. The refined Jensen's inequality is used to prove a Minkowski inequality with upper and lower estimates.
KW - Jensen's inequality
KW - convex functions
KW - concave functions
KW - superadditive functions
KW - subadditive functions .
M3 - Journal article
VL - 47 (95
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
SN - 1220-3874
IS - 1-2
ER -