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An Improved Version of the Parameterized Hardy–Hilbert Inequality Involving Two Partial Sums

Author

Listed:
  • Bicheng Yang

    (Institute of Applied Mathematics, Longyan University, Longyan 364012, China
    School of Mathematics, Guangdong University of Education, Guangzhou 510303, China)

  • Shanhe Wu

    (Institute of Applied Mathematics, Longyan University, Longyan 364012, China)

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.

Suggested Citation

  • Bicheng Yang & Shanhe Wu, 2025. "An Improved Version of the Parameterized Hardy–Hilbert Inequality Involving Two Partial Sums," Mathematics, MDPI, vol. 13(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1331-:d:1637663
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