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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-07-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0041 |
| 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 |