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On a New Extended Hardy–Hilbert’s Inequality with Parameters

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Institute of Applied Mathematics, Lonyan University, Lonyan 364012, China
2
Department of Mathematics, Longyan University, Longyan 364012, China
3
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 73; https://doi.org/10.3390/math8010073
Received: 10 December 2019 / Revised: 30 December 2019 / Accepted: 31 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Inequalities 2020)
In this paper, by introducing parameters and weight functions, with the help of the Euler–Maclaurin summation formula, we establish the extension of Hardy–Hilbert’s inequality and its equivalent forms. The equivalent statements of the best possible constant factor related to several parameters are provided. The operator expressions and some particular cases are also discussed. View Full-Text
Keywords: weight coefficient; Hardy–Hilbert’s inequality; equivalent statement; parameter; operator expression weight coefficient; Hardy–Hilbert’s inequality; equivalent statement; parameter; operator expression
MDPI and ACS Style

Yang, B.; Wu, S.; Liao, J. On a New Extended Hardy–Hilbert’s Inequality with Parameters. Mathematics 2020, 8, 73.

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