On a half-discrete Hilbert-type inequality related to hyperbolic functions

By the introduction of a new half-discrete kernel which is composed of several exponent functions, and using the method of weight coefficient, a Hilbert-type inequality and its equivalent forms involving multiple parameters are established. In addition, it is proved that the constant factors of the...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 16
Main Author You, Minghui
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.09.2021
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Bernoulli number
Half-discrete
Hilbert-type inequality
Hyperbolic functions
Inequalities
Inequality
Mathematical functions
Mathematics
Mathematics and Statistics
Rational fraction expansion
Rational fraction expansion
47B38
26D10
Hilbert-type inequality
Half-discrete
Bernoulli number
Hyperbolic functions
26D15
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Summary:By the introduction of a new half-discrete kernel which is composed of several exponent functions, and using the method of weight coefficient, a Hilbert-type inequality and its equivalent forms involving multiple parameters are established. In addition, it is proved that the constant factors of the newly obtained inequalities are the best possible. Furthermore, by the use of the rational fraction expansion of the tangent function and introducing the Bernoulli numbers, some interesting and special half-discrete Hilbert-type inequalities are presented at the end of the paper.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02688-7