Milne-type inequalities for third differentiable and h-convex functions
Abstract This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p ≥ 1 $p\geq 1$ for s-convexity, convexity, and P-functions class. We examine cases when the...
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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/s13661-024-01984-7 |
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| _version_ | 1841544448770572288 |
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| author | Bouharket Benaissa Hüseyin Budak |
| author_facet | Bouharket Benaissa Hüseyin Budak |
| author_sort | Bouharket Benaissa |
| collection | DOAJ |
| description | Abstract This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p ≥ 1 $p\geq 1$ for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian. |
| format | Article |
| id | doaj-art-91b785bbd19a458f833cc428b9ea3667 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-91b785bbd19a458f833cc428b9ea36672025-01-12T12:33:12ZengSpringerOpenBoundary Value Problems1687-27702025-01-012025111510.1186/s13661-024-01984-7Milne-type inequalities for third differentiable and h-convex functionsBouharket Benaissa0Hüseyin Budak1Faculty of Material Sciences, University of TiaretDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityAbstract This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p ≥ 1 $p\geq 1$ for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.https://doi.org/10.1186/s13661-024-01984-7h-convex functionMilne’s inequalityHölder’s inequalityRiemann’s integral |
| spellingShingle | Bouharket Benaissa Hüseyin Budak Milne-type inequalities for third differentiable and h-convex functions Boundary Value Problems h-convex function Milne’s inequality Hölder’s inequality Riemann’s integral |
| title | Milne-type inequalities for third differentiable and h-convex functions |
| title_full | Milne-type inequalities for third differentiable and h-convex functions |
| title_fullStr | Milne-type inequalities for third differentiable and h-convex functions |
| title_full_unstemmed | Milne-type inequalities for third differentiable and h-convex functions |
| title_short | Milne-type inequalities for third differentiable and h-convex functions |
| title_sort | milne type inequalities for third differentiable and h convex functions |
| topic | h-convex function Milne’s inequality Hölder’s inequality Riemann’s integral |
| url | https://doi.org/10.1186/s13661-024-01984-7 |
| work_keys_str_mv | AT bouharketbenaissa milnetypeinequalitiesforthirddifferentiableandhconvexfunctions AT huseyinbudak milnetypeinequalitiesforthirddifferentiableandhconvexfunctions |