Jensen-type geometric shapes
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2020)
- Volume: 19, page 27-33
- ISSN: 2300-133X
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topPaweł Pasteczka. "Jensen-type geometric shapes." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19 (2020): 27-33. <http://eudml.org/doc/296800>.
@article{PawełPasteczka2020,
abstract = {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.},
author = {Paweł Pasteczka},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Shapes; Platonic shapes; sphere; ball; Jensen's inequality},
language = {eng},
pages = {27-33},
title = {Jensen-type geometric shapes},
url = {http://eudml.org/doc/296800},
volume = {19},
year = {2020},
}
TY - JOUR
AU - Paweł Pasteczka
TI - Jensen-type geometric shapes
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2020
VL - 19
SP - 27
EP - 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.
LA - eng
KW - Shapes; Platonic shapes; sphere; ball; Jensen's inequality
UR - http://eudml.org/doc/296800
ER -
References
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- Niculescu, Constantin P. "The Hermite-Hadamard inequality for convex functions of a vector variable." Math. Inequal. Appl. 5, no. 4 (2002): 619–623.
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