A reverse Hardy–Hilbert-type integral inequality involving one derivative function

Abstract In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. T...

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Main Authors:	Qian Chen, Bicheng Yang
Format:	Article
Language:	English
Published:	SpringerOpen 2020-12-01
Series:	Journal of Inequalities and Applications
Subjects:	Weight function Hardy–Hilbert-type integral inequality Derivative function Parameter Beta function Reverse
Online Access:	https://doi.org/10.1186/s13660-020-02528-0

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spelling	doaj-34ddaf92356d4cf3a74215c74206af4c2020-12-13T12:02:41ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-12-012020111210.1186/s13660-020-02528-0A reverse Hardy–Hilbert-type integral inequality involving one derivative functionQian Chen0Bicheng Yang1Department of Computer Science, Guangdong University of EducationDepartment of Mathematics, Guangdong University of EducationAbstract In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.https://doi.org/10.1186/s13660-020-02528-0Weight functionHardy–Hilbert-type integral inequalityDerivative functionParameterBeta functionReverse
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Qian Chen Bicheng Yang
spellingShingle	Qian Chen Bicheng Yang A reverse Hardy–Hilbert-type integral inequality involving one derivative function Journal of Inequalities and Applications Weight function Hardy–Hilbert-type integral inequality Derivative function Parameter Beta function Reverse
author_facet	Qian Chen Bicheng Yang
author_sort	Qian Chen
title	A reverse Hardy–Hilbert-type integral inequality involving one derivative function
title_short	A reverse Hardy–Hilbert-type integral inequality involving one derivative function
title_full	A reverse Hardy–Hilbert-type integral inequality involving one derivative function
title_fullStr	A reverse Hardy–Hilbert-type integral inequality involving one derivative function
title_full_unstemmed	A reverse Hardy–Hilbert-type integral inequality involving one derivative function
title_sort	reverse hardy–hilbert-type integral inequality involving one derivative function
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2020-12-01
description	Abstract In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.
topic	Weight function Hardy–Hilbert-type integral inequality Derivative function Parameter Beta function Reverse
url	https://doi.org/10.1186/s13660-020-02528-0
work_keys_str_mv	AT qianchen areversehardyhilberttypeintegralinequalityinvolvingonederivativefunction AT bichengyang areversehardyhilberttypeintegralinequalityinvolvingonederivativefunction AT qianchen reversehardyhilberttypeintegralinequalityinvolvingonederivativefunction AT bichengyang reversehardyhilberttypeintegralinequalityinvolvingonederivativefunction
_version_	1724385398088531968

A reverse Hardy–Hilbert-type integral inequality involving one derivative function

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