New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas
Abstract In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02732-6 |
| _version_ | 1818979358727995392 |
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| author | Muhammad Uzair Awan Artion Kashuri Kottakkaran Sooppy Nisar Muhammad Zakria Javed Sabah Iftikhar Poom Kumam Parin Chaipunya |
| author_facet | Muhammad Uzair Awan Artion Kashuri Kottakkaran Sooppy Nisar Muhammad Zakria Javed Sabah Iftikhar Poom Kumam Parin Chaipunya |
| author_sort | Muhammad Uzair Awan |
| collection | DOAJ |
| description | Abstract In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained. |
| first_indexed | 2024-12-20T16:58:16Z |
| format | Article |
| id | doaj.art-8c39bd0d4c2e4fe9bbaf8c9282b43b43 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-20T16:58:16Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-8c39bd0d4c2e4fe9bbaf8c9282b43b432022-12-21T19:32:39ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-01-012022113410.1186/s13660-021-02732-6New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulasMuhammad Uzair Awan0Artion Kashuri1Kottakkaran Sooppy Nisar2Muhammad Zakria Javed3Sabah Iftikhar4Poom Kumam5Parin Chaipunya6Department of Mathematics, Government College UniversityDepartment of Mathematics, Faculty of Technical Science, University “Ismail Qemali”Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityDepartment of Mathematics, Government College UniversityCenter of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT)Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT)Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT)Abstract In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.https://doi.org/10.1186/s13660-021-02732-6Trapezium inequalityHarmonic convex functionRiemann–Liouville fractional integralsHölder inequalityPower mean inequalitySpecial means |
| spellingShingle | Muhammad Uzair Awan Artion Kashuri Kottakkaran Sooppy Nisar Muhammad Zakria Javed Sabah Iftikhar Poom Kumam Parin Chaipunya New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas Journal of Inequalities and Applications Trapezium inequality Harmonic convex function Riemann–Liouville fractional integrals Hölder inequality Power mean inequality Special means |
| title | New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas |
| title_full | New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas |
| title_fullStr | New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas |
| title_full_unstemmed | New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas |
| title_short | New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas |
| title_sort | new fractional identities associated novel fractional inequalities with applications to means and error estimations for quadrature formulas |
| topic | Trapezium inequality Harmonic convex function Riemann–Liouville fractional integrals Hölder inequality Power mean inequality Special means |
| url | https://doi.org/10.1186/s13660-021-02732-6 |
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