A two-point-Padé-approximant-based method for bounding some trigonometric functions

Inequalities are frequently used for solving practical engineering problem. There are two key issues of bounding inequalities; one is to find the bounds, and the other is to prove the bounds. This paper takes Wilker type inequalities as an example, presents a two-point-Padé-approximant-based method...

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Detalles Bibliográficos
Autores principales: Chen, Xiao-Diao, Ma, Junyi, Jin, Jiapei, Wang, Yigang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6010514/
https://www.ncbi.nlm.nih.gov/pubmed/30137727
http://dx.doi.org/10.1186/s13660-018-1726-7
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author Chen, Xiao-Diao
Ma, Junyi
Jin, Jiapei
Wang, Yigang
author_facet Chen, Xiao-Diao
Ma, Junyi
Jin, Jiapei
Wang, Yigang
author_sort Chen, Xiao-Diao
collection PubMed
description Inequalities are frequently used for solving practical engineering problem. There are two key issues of bounding inequalities; one is to find the bounds, and the other is to prove the bounds. This paper takes Wilker type inequalities as an example, presents a two-point-Padé-approximant-based method for finding the bounds, and it also provides a method to prove the bounds in a new way. It not only recovers the estimates in Mortici’s method, but it also provides new improvements of estimates obtained from prevailing methods. In principle, it can be applied for other inequalities.
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spelling pubmed-60105142018-06-25 A two-point-Padé-approximant-based method for bounding some trigonometric functions Chen, Xiao-Diao Ma, Junyi Jin, Jiapei Wang, Yigang J Inequal Appl Research Inequalities are frequently used for solving practical engineering problem. There are two key issues of bounding inequalities; one is to find the bounds, and the other is to prove the bounds. This paper takes Wilker type inequalities as an example, presents a two-point-Padé-approximant-based method for finding the bounds, and it also provides a method to prove the bounds in a new way. It not only recovers the estimates in Mortici’s method, but it also provides new improvements of estimates obtained from prevailing methods. In principle, it can be applied for other inequalities. Springer International Publishing 2018-06-20 2018 /pmc/articles/PMC6010514/ /pubmed/30137727 http://dx.doi.org/10.1186/s13660-018-1726-7 Text en © The Author(s) 2018 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
Chen, Xiao-Diao
Ma, Junyi
Jin, Jiapei
Wang, Yigang
A two-point-Padé-approximant-based method for bounding some trigonometric functions
title A two-point-Padé-approximant-based method for bounding some trigonometric functions
title_full A two-point-Padé-approximant-based method for bounding some trigonometric functions
title_fullStr A two-point-Padé-approximant-based method for bounding some trigonometric functions
title_full_unstemmed A two-point-Padé-approximant-based method for bounding some trigonometric functions
title_short A two-point-Padé-approximant-based method for bounding some trigonometric functions
title_sort two-point-padé-approximant-based method for bounding some trigonometric functions
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6010514/
https://www.ncbi.nlm.nih.gov/pubmed/30137727
http://dx.doi.org/10.1186/s13660-018-1726-7
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