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A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series

Author

Listed:
  • Jianquan Liao
  • Shanhe Wu
  • Bicheng Yang
  • M. M. Bhatti

Abstract

In this study, a multiparameter Hardy–Hilbert-type inequality for double series is established, which contains partial sums as the terms of one of the series. Based on the obtained inequality, we discuss the equivalent statements of the best possible constant factor related to several parameters. Moreover, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:5264623
    DOI: 10.1155/2021/5264623
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    Cited by:

    1. 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.
    2. 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.

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