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Research Article | Open Access

A Hardy-Hilbert-type inequality involving modified weight coefficients and partial sums

Xianyong Huang1, Shanhe Wu2( ), Bicheng Yang3
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
Department of Mathematics, Longyan University, Longyan 364012, China
Institute of Applied Mathematics, Longyan University, Longyan 364012, China
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Abstract

In this article, we construct proper weight coefficients and use them to establish a Hardy-Hilbert-type inequality involving one partial sum. Based on this inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. We also consider the equivalent forms and the operator expressions of the obtained inequalities. At the end of the paper, we demonstrate that more new Hardy-Hilbert-type inequalities can be derived from the special cases of the present results.

Keywords

weight coefficientEuler-Maclaurin summation formulaHardy-Hilbert-type inequalitypartial sumsapplications
CLC number: 26D15, 26D10, 47A05

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6294-6310
DOI: 10.3934/math.2022350

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Cite this article:
Huang X, Wu S, Yang B. A Hardy-Hilbert-type inequality involving modified weight coefficients and partial sums. AIMS Mathematics, 2022, 7(4): 6294-6310. https://doi.org/10.3934/math.2022350

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Received: 30 October 2021
Revised: 14 January 2022
Accepted: 16 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)