On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters

By means of the weight functions, the idea of introduced parameters, and the Euler-Maclaurin summation formula, a reverse half-discrete Hardy-Hilbert’s inequality and the reverse equivalent forms are given. The equivalent statements of the best possible constant factor involving several pa...

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Main Authors:	Bicheng Yang, Shanhe Wu, Aizhen Wang
Format:	Article
Language:	English
Published:	MDPI AG 2019-11-01
Series:	Mathematics
Subjects:	weight function half-discrete hardy-hilbert’s inequality parameter euler-maclaurin summation formula reverse inequality
Online Access:	https://www.mdpi.com/2227-7390/7/11/1054

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spelling	doaj-1b78ef87a35d4307abd7be609068de7e2020-11-24T21:55:32ZengMDPI AGMathematics2227-73902019-11-01711105410.3390/math7111054math7111054On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with ParametersBicheng Yang0Shanhe Wu1Aizhen Wang2Institute of Applied Mathematics, Longyan University, Longyan 364012, ChinaDepartment of Mathematics, Longyan University, Longyan 364012, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaBy means of the weight functions, the idea of introduced parameters, and the Euler-Maclaurin summation formula, a reverse half-discrete Hardy-Hilbert’s inequality and the reverse equivalent forms are given. The equivalent statements of the best possible constant factor involving several parameters are considered. As applications, two results related to the case of the non-homogeneous kernel and some particular cases are obtained.https://www.mdpi.com/2227-7390/7/11/1054weight functionhalf-discrete hardy-hilbert’s inequalityparametereuler-maclaurin summation formulareverse inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bicheng Yang Shanhe Wu Aizhen Wang
spellingShingle	Bicheng Yang Shanhe Wu Aizhen Wang On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters Mathematics weight function half-discrete hardy-hilbert’s inequality parameter euler-maclaurin summation formula reverse inequality
author_facet	Bicheng Yang Shanhe Wu Aizhen Wang
author_sort	Bicheng Yang
title	On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters
title_short	On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters
title_full	On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters
title_fullStr	On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters
title_full_unstemmed	On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters
title_sort	on a reverse half-discrete hardy-hilbert’s inequality with parameters
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-11-01
description	By means of the weight functions, the idea of introduced parameters, and the Euler-Maclaurin summation formula, a reverse half-discrete Hardy-Hilbert’s inequality and the reverse equivalent forms are given. The equivalent statements of the best possible constant factor involving several parameters are considered. As applications, two results related to the case of the non-homogeneous kernel and some particular cases are obtained.
topic	weight function half-discrete hardy-hilbert’s inequality parameter euler-maclaurin summation formula reverse inequality
url	https://www.mdpi.com/2227-7390/7/11/1054
work_keys_str_mv	AT bichengyang onareversehalfdiscretehardyhilbertsinequalitywithparameters AT shanhewu onareversehalfdiscretehardyhilbertsinequalitywithparameters AT aizhenwang onareversehalfdiscretehardyhilbertsinequalitywithparameters
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On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters

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