Jensen-type geometric shapes

Paweł Pasteczka

doi:10.2478/aupcsm-2020-0002

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Jensen-type geometric shapes

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 19 (2020): Issue 1 (December 2020)

By: Paweł Pasteczka

Open Access

|Dec 2020

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2020-0002 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 27 - 33

Submitted on: May 7, 2019

Accepted on: Aug 26, 2019

Published on: Dec 31, 2020

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Shapes,

Platonic shapes,

sphere,

ball,

Jensen’s inequality

Related subjects:

Mathematics,

General mathematics

© 2020 Paweł Pasteczka, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 19 (2020): Issue 1 (December 2020)