A new reverse Hardy–Hilbert inequality with the power function as intermediate variables
Abstract In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients and use them to establish a reverse Hardy–Hilbert inequality with the power function as intermediate variables. Then, w...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02784-2 |
| _version_ | 1818013560644567040 |
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| author | Xingshou Huang Bicheng Yang Ricai Luo |
| author_facet | Xingshou Huang Bicheng Yang Ricai Luo |
| author_sort | Xingshou Huang |
| collection | DOAJ |
| description | Abstract In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients and use them to establish a reverse Hardy–Hilbert inequality with the power function as intermediate variables. Then, we obtain the equivalent forms and some equivalent statements of the best possible constant factor related to several parameters. Finally, we illustrate how the obtained results can generate some particular reverse Hardy–Hilbert inequalities. |
| first_indexed | 2024-04-14T06:34:43Z |
| format | Article |
| id | doaj.art-afd88f4059cc4c22923560777940980d |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-14T06:34:43Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-afd88f4059cc4c22923560777940980d2022-12-22T02:07:30ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-04-012022111610.1186/s13660-022-02784-2A new reverse Hardy–Hilbert inequality with the power function as intermediate variablesXingshou Huang0Bicheng Yang1Ricai Luo2School of Mathematics and Statistics, Hechi UniversityDepartment of Mathematics, Guangdong University of EducationSchool of Mathematics and Statistics, Hechi UniversityAbstract In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients and use them to establish a reverse Hardy–Hilbert inequality with the power function as intermediate variables. Then, we obtain the equivalent forms and some equivalent statements of the best possible constant factor related to several parameters. Finally, we illustrate how the obtained results can generate some particular reverse Hardy–Hilbert inequalities.https://doi.org/10.1186/s13660-022-02784-2Weight coefficientHardy–Hilbert inequalityEquivalent statementParameterPower functionReverse |
| spellingShingle | Xingshou Huang Bicheng Yang Ricai Luo A new reverse Hardy–Hilbert inequality with the power function as intermediate variables Journal of Inequalities and Applications Weight coefficient Hardy–Hilbert inequality Equivalent statement Parameter Power function Reverse |
| title | A new reverse Hardy–Hilbert inequality with the power function as intermediate variables |
| title_full | A new reverse Hardy–Hilbert inequality with the power function as intermediate variables |
| title_fullStr | A new reverse Hardy–Hilbert inequality with the power function as intermediate variables |
| title_full_unstemmed | A new reverse Hardy–Hilbert inequality with the power function as intermediate variables |
| title_short | A new reverse Hardy–Hilbert inequality with the power function as intermediate variables |
| title_sort | new reverse hardy hilbert inequality with the power function as intermediate variables |
| topic | Weight coefficient Hardy–Hilbert inequality Equivalent statement Parameter Power function Reverse |
| url | https://doi.org/10.1186/s13660-022-02784-2 |
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