<abstract xmlns="http://www.w3.org/1999/xhtml">Each family <italic>ℳ</italic> of means has a natural, partial order (point-wise order), that is <italic>M ≤ N</italic> iff <italic>M</italic>(<italic>x</italic>) <italic>≤ N</italic>(<italic>x</italic>) for all admissible <italic>x</italic>.In this setting we can introduce the notion of interval-type set (a subset <italic>ℐ ⊂ℳ</italic> such that whenever <italic>M ≤ P ≤ N</italic> for some <italic>M, N ∈ℐ</italic> and <italic>P ∈ℳ</italic> then <italic>P ∈ℐ</italic>). For example, in the case of power means there exists a natural isomorphism between interval-type sets and intervals contained in real numbers. Nevertheless there appear a number of interesting objects for a families which cannot be linearly ordered.In the present paper we consider this property for Gini means and Hardy means. Moreover, some results concerning <italic>L</italic>∞ metric among (abstract) means will be obtained.</abstract>

Each family ℳ of means has a natural, partial order (point-wise order), that is M ≤ N iff M(x) ≤ N(x) for all admissible x.In this setting we can introduce the notion of interval-type set (a subset ℐ ⊂ℳ such that whenever M ≤ P ≤ N for some M, N ∈ℐ and P ∈ℳ then P ∈ℐ). For example, in the case of power means there exists a natural isomorphism between interval-type sets and intervals contained in real numbers. Nevertheless there appear a number of interesting objects for a families which cannot be linearly ordered.In the present paper we consider this property for Gini means and Hardy means. Moreover, some results concerning L∞ metric among (abstract) means will be obtained.

Interval-type theorems concerning means

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Interval-type theorems concerning means"}

Each family ℳ of means has a natural, partial order (point-wise order), that is M ≤ N iff M(x) ≤ N(x) for all admissible x.In this setting we can introduce the...

Interval-type theorems concerning means

Online veröffentlicht: 23. Feb. 2019

Seitenbereich: 37 - 43

Eingereicht: 04. Jan. 2018

Akzeptiert: 30. März 2018

DOI: https://doi.org/10.2478/aupcsm-2018-0004

Schlüsselwörter
and phrases: means, squeeze theorem, sandwich theorems, distance between means, Hardy means

© 2018 Paweł Pasteczka, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Interval-type theorems concerning means

Online veröffentlicht: 23. Feb. 2019

Seitenbereich: 37 - 43

Eingereicht: 04. Jan. 2018

Akzeptiert: 30. März 2018

DOI: https://doi.org/10.2478/aupcsm-2018-0004

Schlüsselwörterand phrases: means, squeeze theorem, sandwich theorems, distance between means, Hardy means

© 2018 Paweł Pasteczka, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Schlüsselwörter
and phrases: means, squeeze theorem, sandwich theorems, distance between means, Hardy means