New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals
In this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are s-convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions who...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1997549 |
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| author | Khuram Ali Khan Saeeda Fatima Ammara Nosheen Rostin Matendo Mabela |
| author_facet | Khuram Ali Khan Saeeda Fatima Ammara Nosheen Rostin Matendo Mabela |
| author_sort | Khuram Ali Khan |
| collection | DOAJ |
| description | In this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are s-convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions whose absolute values of second derivatives are s-convex are also established with the help of an existing identity in literature. Many limiting results are deduced from the main results which are stated in remarks. Some applications of proved results are also discussed in the present study. |
| format | Article |
| id | doaj-art-2e9053d4d3a444889ad7621872302a57 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2e9053d4d3a444889ad7621872302a572025-02-03T01:29:32ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/1997549New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional IntegralsKhuram Ali Khan0Saeeda Fatima1Ammara Nosheen2Rostin Matendo Mabela3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Maths and Computer ScienceIn this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are s-convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions whose absolute values of second derivatives are s-convex are also established with the help of an existing identity in literature. Many limiting results are deduced from the main results which are stated in remarks. Some applications of proved results are also discussed in the present study.http://dx.doi.org/10.1155/2024/1997549 |
| spellingShingle | Khuram Ali Khan Saeeda Fatima Ammara Nosheen Rostin Matendo Mabela New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals Journal of Mathematics |
| title | New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals |
| title_full | New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals |
| title_fullStr | New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals |
| title_full_unstemmed | New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals |
| title_short | New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals |
| title_sort | new developments of hermite hadamard type inequalities via s convexity and fractional integrals |
| url | http://dx.doi.org/10.1155/2024/1997549 |
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