TY - JOUR
AU - Pasteczka, PaweÅ‚
PY - 2020/01/01
Y2 - 2023/12/06
TI - Jensen-type geometric shapes
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 19
IS -
SE - Published
DO -
UR - https://studmath.up.krakow.pl/article/view/7120
SP - 27-33
AB - We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.
ER -