A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum

In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin s...

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Main Authors:	Xianyong Huang, Shanhe Wu, Bicheng Yang
Format:	Article
Language:	English
Published:	MDPI AG 2021-08-01
Series:	Symmetry
Subjects:	weight coefficient Euler–Maclaurin summation formula Abel’s partial summation formula half-discrete Hilbert-type inequality upper limit function
Online Access:	https://www.mdpi.com/2073-8994/13/8/1548

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spelling	doaj-e5564b580d1c4a52942e40a718f1169d2021-08-26T14:24:26ZengMDPI AGSymmetry2073-89942021-08-01131548154810.3390/sym13081548A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial SumXianyong Huang0Shanhe Wu1Bicheng Yang2Department of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Longyan University, Longyan 364012, ChinaInstitute of Applied Mathematics, Longyan University, Longyan 364012, ChinaIn this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.https://www.mdpi.com/2073-8994/13/8/1548weight coefficientEuler–Maclaurin summation formulaAbel’s partial summation formulahalf-discrete Hilbert-type inequalityupper limit function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xianyong Huang Shanhe Wu Bicheng Yang
spellingShingle	Xianyong Huang Shanhe Wu Bicheng Yang A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum Symmetry weight coefficient Euler–Maclaurin summation formula Abel’s partial summation formula half-discrete Hilbert-type inequality upper limit function
author_facet	Xianyong Huang Shanhe Wu Bicheng Yang
author_sort	Xianyong Huang
title	A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
title_short	A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
title_full	A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
title_fullStr	A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
title_full_unstemmed	A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
title_sort	more accurate half-discrete hilbert-type inequality involving one upper limit function and one partial sum
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2021-08-01
description	In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.
topic	weight coefficient Euler–Maclaurin summation formula Abel’s partial summation formula half-discrete Hilbert-type inequality upper limit function
url	https://www.mdpi.com/2073-8994/13/8/1548
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A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum

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