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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Bicheng Yang & Shanhe Wu & Xingshou Huang, 2022. "A Reverse Hardy–Hilbert’s Inequality Containing Multiple Parameters and One Partial Sum," Mathematics, MDPI, vol. 10(13), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2362-:d:856457
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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.
    2. Bicheng Yang & Shanhe Wu & Qiang Chen, 2020. "A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
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