Estimating the Hardy Constant of Nonconcave Homogeneous Quasideviation Means

Zsolt Páles; Paweł Pasteczka

doi:10.2478/amsil-2024-0004

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Estimating the Hardy Constant of Nonconcave Homogeneous Quasideviation Means

Annales Mathematicae Silesianae

Volume 38 (2024): Issue 1 (March 2024)

By: Zsolt Páles and Paweł Pasteczka

Open Access

|Feb 2024

Abstract

In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely determined. Using this description, we establish su˚cient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2024-0004 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 78 - 92

Submitted on: Jul 21, 2023

Accepted on: Jan 24, 2024

Published on: Feb 15, 2024

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Hardy inequality,

Hardy constant,

homogeneous quasideviation mean,

Jensen concavity

Related subjects:

Mathematics,

General mathematics

© 2024 Zsolt Páles, Paweł Pasteczka, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 38 (2024): Issue 1 (March 2024)