Optimal inequalities for bounding Toader mean by arithmetic and quadratic means

In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text] , and we provide new bounds for the complete elliptic integral [Fo...

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Detalles Bibliográficos
Autores principales: Zhao, Tie-Hong, Chu, Yu-Ming, Zhang, Wen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5266785/
https://www.ncbi.nlm.nih.gov/pubmed/28190939
http://dx.doi.org/10.1186/s13660-017-1300-8
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author Zhao, Tie-Hong
Chu, Yu-Ming
Zhang, Wen
author_facet Zhao, Tie-Hong
Chu, Yu-Ming
Zhang, Wen
author_sort Zhao, Tie-Hong
collection PubMed
description In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text] , and we provide new bounds for the complete elliptic integral [Formula: see text] [Formula: see text] of the second kind, where [Formula: see text] , [Formula: see text] and [Formula: see text] are the Toader, arithmetic, and quadratic means of a and b, respectively.
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spelling pubmed-52667852017-02-09 Optimal inequalities for bounding Toader mean by arithmetic and quadratic means Zhao, Tie-Hong Chu, Yu-Ming Zhang, Wen J Inequal Appl Research In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text] , and we provide new bounds for the complete elliptic integral [Formula: see text] [Formula: see text] of the second kind, where [Formula: see text] , [Formula: see text] and [Formula: see text] are the Toader, arithmetic, and quadratic means of a and b, respectively. Springer International Publishing 2017-01-25 2017 /pmc/articles/PMC5266785/ /pubmed/28190939 http://dx.doi.org/10.1186/s13660-017-1300-8 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
Zhao, Tie-Hong
Chu, Yu-Ming
Zhang, Wen
Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
title Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
title_full Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
title_fullStr Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
title_full_unstemmed Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
title_short Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
title_sort optimal inequalities for bounding toader mean by arithmetic and quadratic means
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5266785/
https://www.ncbi.nlm.nih.gov/pubmed/28190939
http://dx.doi.org/10.1186/s13660-017-1300-8
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