1. bookVolume 19 (2020): Edition 1 (December 2020)
Détails du magazine
License
Format
Magazine
eISSN
2300-133X
ISSN
2081-545X
Première parution
11 Dec 2014
Périodicité
1 fois par an
Langues
Anglais
access type Accès libre

Jensen-type geometric shapes

Publié en ligne: 31 Dec 2020
Volume & Edition: Volume 19 (2020) - Edition 1 (December 2020)
Pages: 27 - 33
Reçu: 07 May 2019
Accepté: 26 Aug 2019
Détails du magazine
License
Format
Magazine
eISSN
2300-133X
ISSN
2081-545X
Première parution
11 Dec 2014
Périodicité
1 fois par an
Langues
Anglais
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.

Keywords

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