A Weighted Generalization of Hardy–Hilbert-Type Inequality Involving Two Partial Sums

Bicheng Yang and Shanhe Wu ()
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Bicheng Yang: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Shanhe Wu: Institute of Applied Mathematics, Longyan University, Longyan 364012, China

Mathematics, 2023, vol. 11, issue 14, 1-13

Abstract: In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial summation formula, and differential mean value theorem, a new weighted Hardy–Hilbert-type inequality containing two partial sums can be proven, which is a further generalization of an existing result. Based on the obtained results, we provide the equivalent statements of the best possible constant factor related to several parameters. Also, we illustrate how the inequalities obtained in the main results can generate some new Hardy–Hilbert-type inequalities.

Keywords: Hardy–Hilbert-type inequality; partial sum; parameter; Abel’s partial summation formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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