A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/8/1548 |
| _version_ | 1797521966592163840 |
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| author | Xianyong Huang Shanhe Wu Bicheng Yang |
| author_facet | Xianyong Huang Shanhe Wu Bicheng Yang |
| author_sort | Xianyong Huang |
| collection | DOAJ |
| description | In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities. |
| first_indexed | 2024-03-10T08:20:02Z |
| format | Article |
| id | doaj.art-e5564b580d1c4a52942e40a718f1169d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:20:02Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e5564b580d1c4a52942e40a718f1169d2023-11-22T10:03:18ZengMDPI AGSymmetry2073-89942021-08-01138154810.3390/sym13081548A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial SumXianyong Huang0Shanhe Wu1Bicheng Yang2Department of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Longyan University, Longyan 364012, ChinaInstitute of Applied Mathematics, Longyan University, Longyan 364012, ChinaIn this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.https://www.mdpi.com/2073-8994/13/8/1548weight coefficientEuler–Maclaurin summation formulaAbel’s partial summation formulahalf-discrete Hilbert-type inequalityupper limit function |
| spellingShingle | Xianyong Huang Shanhe Wu Bicheng Yang A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum Symmetry weight coefficient Euler–Maclaurin summation formula Abel’s partial summation formula half-discrete Hilbert-type inequality upper limit function |
| title | A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum |
| title_full | A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum |
| title_fullStr | A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum |
| title_full_unstemmed | A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum |
| title_short | A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum |
| title_sort | more accurate half discrete hilbert type inequality involving one upper limit function and one partial sum |
| topic | weight coefficient Euler–Maclaurin summation formula Abel’s partial summation formula half-discrete Hilbert-type inequality upper limit function |
| url | https://www.mdpi.com/2073-8994/13/8/1548 |
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