1. bookVolume 19 (2020): Issue 1 (December 2020)
Journal Details
License
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Journal
First Published
11 Dec 2014
Publication timeframe
1 time per year
Languages
English
access type Open Access

Jensen-type geometric shapes

Published Online: 31 Dec 2020
Page range: 27 - 33
Received: 07 May 2019
Accepted: 26 Aug 2019
Journal Details
License
Format
Journal
First Published
11 Dec 2014
Publication timeframe
1 time per year
Languages
English
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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