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Chen, Qian; Yang, Bicheng

A reverse Hardy-Hilbert-type integral inequality involving one derivative function. (English) Zbl 1503.26046

J. Inequal. Appl. 2020, Paper No. 259, 12 p. (2020).
Summary: In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy-Hilbert integral inequality and the techniques of real analysis, a reverse Hardy-Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

MSC:

26D15 Inequalities for sums, series and integrals
33B15 Gamma, beta and polygamma functions

Keywords:

weight function; Hardy-Hilbert-type integral inequality; derivative function; parameter; beta function; reverse
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References:

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