On a new generalization of some Hilbert-type inequalities

In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also c...

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Published inOpen mathematics (Warsaw, Poland) Vol. 19; no. 1; pp. 569 - 582
Main Authors You, Minghui, Song, Wei, Wang, Xiaoyu
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 09.07.2021
De Gruyter Poland
Subjects
26D15
41A17
Bernoulli number
Euler number
Hilbert-type inequality
Inequalities
Kernel functions
partial fraction expansion
Trigonometric functions
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Summary:In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2391-5455
2391-5455
DOI:10.1515/math-2021-0034