Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text] , where [Formula: see text] , [Formula: see text] and [Fo...

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Detalles Bibliográficos
Autores principales: Ding, Qing, Zhao, Tiehong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5420009/
https://www.ncbi.nlm.nih.gov/pubmed/28539752
http://dx.doi.org/10.1186/s13660-017-1365-4
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author Ding, Qing
Zhao, Tiehong
author_facet Ding, Qing
Zhao, Tiehong
author_sort Ding, Qing
collection PubMed
description In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text] , where [Formula: see text] , [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two positive numbers a and b, respectively.
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spelling pubmed-54200092017-05-22 Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean Ding, Qing Zhao, Tiehong J Inequal Appl Research In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text] , where [Formula: see text] , [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two positive numbers a and b, respectively. Springer International Publishing 2017-05-05 2017 /pmc/articles/PMC5420009/ /pubmed/28539752 http://dx.doi.org/10.1186/s13660-017-1365-4 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Ding, Qing
Zhao, Tiehong
Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
title Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
title_full Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
title_fullStr Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
title_full_unstemmed Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
title_short Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
title_sort optimal bounds for arithmetic-geometric and toader means in terms of generalized logarithmic mean
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5420009/
https://www.ncbi.nlm.nih.gov/pubmed/28539752
http://dx.doi.org/10.1186/s13660-017-1365-4
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