<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p><p>It is proved that this inequality holds for <italic>n</italic>-dimensional parallelotopes, <italic>n-</italic>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.</p></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.

Jensen-type geometric shapes

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Jensen-type geometric shapes"}

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...

Jensen-type geometric shapes

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

Parole chiave
Shapes, Platonic shapes, sphere, ball, Jensen’s inequality

© 2020 Paweł Pasteczka, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Jensen-type geometric shapes

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

Parole chiaveShapes, Platonic shapes, sphere, ball, Jensen’s inequality

© 2020 Paweł Pasteczka, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Parole chiave
Shapes, Platonic shapes, sphere, ball, Jensen’s inequality