An Improved Version of the Parameterized Hardy–Hilbert 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, 2025, vol. 13, issue 8, 1-14

Abstract: In this paper, by employing the Euler–Maclaurin summation formula and real analysis techniques, an improved version of the parameterized Hardy–Hilbert inequality involving two partial sums is established. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. Our results extend the classical Hardy–Hilbert inequality and improve certain existing results.

Keywords: Hardy–Hilbert inequality; multiple parameters; partial sums; equivalent conditions; best possible constant factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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