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Open AccessArticle

On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters

1
Institute of Applied Mathematics, Longyan University, Longyan 364012, China
2
Department of Mathematics, Longyan University, Longyan 364012, China
3
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1054; https://doi.org/10.3390/math7111054
Received: 22 August 2019 / Revised: 26 October 2019 / Accepted: 29 October 2019 / Published: 4 November 2019
(This article belongs to the Special Issue Inequalities)
By means of the weight functions, the idea of introduced parameters, and the Euler-Maclaurin summation formula, a reverse half-discrete Hardy-Hilbert’s inequality and the reverse equivalent forms are given. The equivalent statements of the best possible constant factor involving several parameters are considered. As applications, two results related to the case of the non-homogeneous kernel and some particular cases are obtained. View Full-Text
Keywords: weight function; half-discrete Hardy-Hilbert’s inequality; parameter; Euler-Maclaurin summation formula; reverse inequality weight function; half-discrete Hardy-Hilbert’s inequality; parameter; Euler-Maclaurin summation formula; reverse inequality
MDPI and ACS Style

Yang, B.; Wu, S.; Wang, A. On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters. Mathematics 2019, 7, 1054.

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