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

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  • 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, 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.

Suggested Citation

  • Bicheng Yang & Shanhe Wu, 2023. "A Weighted Generalization of Hardy–Hilbert-Type Inequality Involving Two Partial Sums," Mathematics, MDPI, vol. 11(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3212-:d:1199749
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    References listed on IDEAS

    as
    1. Jianquan Liao & Shanhe Wu & Bicheng Yang & M. M. Bhatti, 2021. "A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, December.
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