On a more accurate half-discrete Hilbert-type inequality involving hyperbolic functions

In this work, by the introduction of a new kernel function composed of exponent functions with several parameters, and using the method of weight coefficient, Hermite-Hadamard’s inequality, and some other techniques of real analysis, a more accurate half-discrete Hilbert-type inequality including bo...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 20; no. 1; pp. 544 - 559
Main Authors You, Minghui, Sun, Xia, Fan, Xiansheng
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 27.07.2022
De Gruyter Poland
Subjects
26D15
41A17
Bernoulli number
Hermite-Hadamard’s inequality
Hilbert-type inequality
hyperbolic function
Hyperbolic functions
Inequalities
Kernel functions
rational fraction expansion
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Summary:In this work, by the introduction of a new kernel function composed of exponent functions with several parameters, and using the method of weight coefficient, Hermite-Hadamard’s inequality, and some other techniques of real analysis, a more accurate half-discrete Hilbert-type inequality including both the homogeneous and non-homogeneous cases is established. Furthermore, by introducing the Bernoulli number and the rational fraction expansion of tangent function, some special and interesting Hilbert-type inequalities and their equivalent hardy-type inequalities are presented at the end of the paper.
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ISSN:2391-5455
2391-5455
DOI:10.1515/math-2022-0041