Interval-type theorems concerning means-Reference-Cited by-同舟云学术

Interval-type theorems concerning means

Published:2018-12-01 Issue:1 Volume:17 Page:37-43
ISSN:2300-133X
Container-title:Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
language:en
Short-container-title:

Author:

Pasteczka Paweł¹

Affiliation:

1. Institute of Mathematics Pedagogical, University of Cracow , Podchorążych str. 2 30-084 Kraków Poland

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/aupcsm-2018-0004

Reference17 articles.

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1. Interval-type theorems concerning quasi-arithmetic means;Mathematical Inequalities & Applications;2019