On a new generalization of some Hilbert-type inequalities

In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also c...

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Autores principales:	You Minghui, Song Wei, Wang Xiaoyu
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	hilbert-type inequality partial fraction expansion euler number bernoulli number 26d15 41a17 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6002cd32271f42bfa878693421e38e22
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spelling	oai:doaj.org-article:6002cd32271f42bfa878693421e38e222021-12-05T14:10:53ZOn a new generalization of some Hilbert-type inequalities2391-545510.1515/math-2021-0034https://doaj.org/article/6002cd32271f42bfa878693421e38e222021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0034https://doaj.org/toc/2391-5455In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.You MinghuiSong WeiWang XiaoyuDe Gruyterarticlehilbert-type inequalitypartial fraction expansioneuler numberbernoulli number26d1541a17MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 569-582 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	hilbert-type inequality partial fraction expansion euler number bernoulli number 26d15 41a17 Mathematics QA1-939
spellingShingle	hilbert-type inequality partial fraction expansion euler number bernoulli number 26d15 41a17 Mathematics QA1-939 You Minghui Song Wei Wang Xiaoyu On a new generalization of some Hilbert-type inequalities
description	In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.
format	article
author	You Minghui Song Wei Wang Xiaoyu
author_facet	You Minghui Song Wei Wang Xiaoyu
author_sort	You Minghui
title	On a new generalization of some Hilbert-type inequalities
title_short	On a new generalization of some Hilbert-type inequalities
title_full	On a new generalization of some Hilbert-type inequalities
title_fullStr	On a new generalization of some Hilbert-type inequalities
title_full_unstemmed	On a new generalization of some Hilbert-type inequalities
title_sort	on a new generalization of some hilbert-type inequalities
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/6002cd32271f42bfa878693421e38e22
work_keys_str_mv	AT youminghui onanewgeneralizationofsomehilberttypeinequalities AT songwei onanewgeneralizationofsomehilberttypeinequalities AT wangxiaoyu onanewgeneralizationofsomehilberttypeinequalities
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On a new generalization of some Hilbert-type inequalities

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