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

Bicheng Yang, Shanhe Wu and Jianquan Liao
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Bicheng Yang: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Shanhe Wu: Department of Mathematics, Longyan University, Longyan 364012, China
Jianquan Liao: Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Mathematics, 2020, vol. 8, issue 1, 1-12

Abstract: 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.

Keywords: weight coefficient; Hardy–Hilbert’s inequality; equivalent statement; parameter; operator expression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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