A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals
This paper deals with a new sharp version of Simpson’s second inequality by using the concepts of absolute continuity, Grüss inequality, and Chebyshev functionals. To demonstrate the applicability of the main result, three examples are given. Also, as generalization of the main result, a Simpson’s s...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/6411956 |
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| _version_ | 1849388220127641600 |
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| author | Mohsen Rostamian Delavar |
| author_facet | Mohsen Rostamian Delavar |
| author_sort | Mohsen Rostamian Delavar |
| collection | DOAJ |
| description | This paper deals with a new sharp version of Simpson’s second inequality by using the concepts of absolute continuity, Grüss inequality, and Chebyshev functionals. To demonstrate the applicability of the main result, three examples are given. Also, as generalization of the main result, a Simpson’s second type inequality related to the class of Riemann–Liouville fractional integrals is obtained. In addition, Simpson’s 3/8 formula is applied to approximate the Riemann integral of an absolutely continuous function as well as estimation of approximation error. |
| format | Article |
| id | doaj-art-724bf2ea74d84943b37390309f4bcbba |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-724bf2ea74d84943b37390309f4bcbba2025-08-20T03:42:22ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/6411956A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional IntegralsMohsen Rostamian Delavar0Department of MathematicsThis paper deals with a new sharp version of Simpson’s second inequality by using the concepts of absolute continuity, Grüss inequality, and Chebyshev functionals. To demonstrate the applicability of the main result, three examples are given. Also, as generalization of the main result, a Simpson’s second type inequality related to the class of Riemann–Liouville fractional integrals is obtained. In addition, Simpson’s 3/8 formula is applied to approximate the Riemann integral of an absolutely continuous function as well as estimation of approximation error.http://dx.doi.org/10.1155/jom/6411956 |
| spellingShingle | Mohsen Rostamian Delavar A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals Journal of Mathematics |
| title | A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals |
| title_full | A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals |
| title_fullStr | A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals |
| title_full_unstemmed | A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals |
| title_short | A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals |
| title_sort | sharp simpson s second type inequality via riemann liouville fractional integrals |
| url | http://dx.doi.org/10.1155/jom/6411956 |
| work_keys_str_mv | AT mohsenrostamiandelavar asharpsimpsonssecondtypeinequalityviariemannliouvillefractionalintegrals AT mohsenrostamiandelavar sharpsimpsonssecondtypeinequalityviariemannliouvillefractionalintegrals |