A Reverse Hardy–Hilbert’s Inequality Containing Multiple Parameters and One Partial Sum

Bicheng Yang, Shanhe Wu and Xingshou Huang
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Bicheng Yang: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Shanhe Wu: Department of Mathematics, Longyan University, Longyan 364012, China
Xingshou Huang: School of Mathematics and Statistics, Hechi University, Yizhou 546300, China

Mathematics, 2022, vol. 10, issue 13, 1-13

Abstract: In this work, by introducing multiple parameters and utilizing the Euler–Maclaurin summation formula and Abel’s partial summation formula, we first establish a reverse Hardy–Hilbert’s inequality containing one partial sum as the terms of double series. Then, based on the newly proposed inequality, we characterize the equivalent conditions of the best possible constant factor associated with several parameters. At the end of the paper, we illustrate that more new inequalities can be generated from the special cases of the reverse Hardy–Hilbert’s inequality.

Keywords: reverse Hardy–Hilbert’s inequality; partial sum; multiple parameters; best possible constant factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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