Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals
Abstract In this research article, equality is proved to obtain corrected Euler–Maclaurin-type inequalities. Using this identity, we establish several corrected Euler–Maclaurin-type inequalities for the case of differentiable convex functions by means of conformable fractional integrals. Moreover, s...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-024-01990-9 |
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| _version_ | 1841544466322685952 |
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| author | Yaren Acar Hüseyin Budak Umut Bas Fatih Hezenci Hüseyin Yıldırım |
| author_facet | Yaren Acar Hüseyin Budak Umut Bas Fatih Hezenci Hüseyin Yıldırım |
| author_sort | Yaren Acar |
| collection | DOAJ |
| description | Abstract In this research article, equality is proved to obtain corrected Euler–Maclaurin-type inequalities. Using this identity, we establish several corrected Euler–Maclaurin-type inequalities for the case of differentiable convex functions by means of conformable fractional integrals. Moreover, some corrected Euler–Maclaurin-type inequalities are given for bounded functions by fractional integrals. Additionally, fractional corrected Euler–Maclaurin-type inequalities are constructed for Lipschitzian functions. Finally, corrected Euler–Maclaurin-type inequalities are considered by fractional integrals of bounded variation. |
| format | Article |
| id | doaj-art-cd10934943e246b4a2dcfb02097f0027 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-cd10934943e246b4a2dcfb02097f00272025-01-12T12:33:14ZengSpringerOpenBoundary Value Problems1687-27702025-01-012025113010.1186/s13661-024-01990-9Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integralsYaren Acar0Hüseyin Budak1Umut Bas2Fatih Hezenci3Hüseyin Yıldırım4Department of Mathematics, Faculty of Science and Arts, Duzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Kahramanmaras Sutcu Imam UnýversýtyDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Kahramanmaras Sutcu Imam UnýversýtyAbstract In this research article, equality is proved to obtain corrected Euler–Maclaurin-type inequalities. Using this identity, we establish several corrected Euler–Maclaurin-type inequalities for the case of differentiable convex functions by means of conformable fractional integrals. Moreover, some corrected Euler–Maclaurin-type inequalities are given for bounded functions by fractional integrals. Additionally, fractional corrected Euler–Maclaurin-type inequalities are constructed for Lipschitzian functions. Finally, corrected Euler–Maclaurin-type inequalities are considered by fractional integrals of bounded variation.https://doi.org/10.1186/s13661-024-01990-9Quadrature formulaeCorrected Maclaurin’s formulaFractional calculusConformable fractional integrals |
| spellingShingle | Yaren Acar Hüseyin Budak Umut Bas Fatih Hezenci Hüseyin Yıldırım Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals Boundary Value Problems Quadrature formulae Corrected Maclaurin’s formula Fractional calculus Conformable fractional integrals |
| title | Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals |
| title_full | Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals |
| title_fullStr | Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals |
| title_full_unstemmed | Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals |
| title_short | Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals |
| title_sort | advancements in corrected euler maclaurin type inequalities via conformable fractional integrals |
| topic | Quadrature formulae Corrected Maclaurin’s formula Fractional calculus Conformable fractional integrals |
| url | https://doi.org/10.1186/s13661-024-01990-9 |
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