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On a new generalization of some Hilbert-type inequalities
- Source :
- Open Mathematics, Vol 19, Iss 1, Pp 569-582 (2021)
- Publication Year :
- 2021
- Publisher :
- De Gruyter, 2021.
-
Abstract
- 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.
- Subjects :
- Pure mathematics
Inequality
41a17
Generalization
hilbert-type inequality
General Mathematics
media_common.quotation_subject
010102 general mathematics
Type (model theory)
Partial fraction decomposition
01 natural sciences
010101 applied mathematics
symbols.namesake
26d15
partial fraction expansion
symbols
QA1-939
euler number
0101 mathematics
Euler number
Bernoulli number
Mathematics
media_common
bernoulli number
Subjects
Details
- Language :
- English
- ISSN :
- 23915455
- Volume :
- 19
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Open Mathematics
- Accession number :
- edsair.doi.dedup.....3495fab07a49fa456dbbc14665e2a7ed