1. bookVolumen 19 (2020): Heft 1 (December 2020)
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
2300-133X
ISSN
2081-545X
Erstveröffentlichung
11 Dec 2014
Erscheinungsweise
1 Hefte pro Jahr
Sprachen
Englisch
access type Uneingeschränkter Zugang

Jensen-type geometric shapes

Online veröffentlicht: 31 Dec 2020
Volumen & Heft: Volumen 19 (2020) - Heft 1 (December 2020)
Seitenbereich: 27 - 33
Eingereicht: 07 May 2019
Akzeptiert: 26 Aug 2019
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
2300-133X
ISSN
2081-545X
Erstveröffentlichung
11 Dec 2014
Erscheinungsweise
1 Hefte pro Jahr
Sprachen
Englisch
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.

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