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Jensen-type geometric shapes

Paweł Pasteczka
Paweł Pasteczka
   | 31 dic 2020
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica's Cover Image
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Pubblicato online: 31 dic 2020
Pagine: 27 - 33
Ricevuto: 07 mag 2019
Accettato: 26 ago 2019
DOI: https://doi.org/10.2478/aupcsm-2020-0002
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© 2020 Paweł Pasteczka, published by Sciendo
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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.

eISSN:
2300-133X
ISSN:
2081-545X
Lingua:
Inglese
Frequenza di pubblicazione:
Volume Open
Argomenti della rivista:
Mathematics, General Mathematics
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