Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators
Abstract In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of ψ-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish so...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02001-1 |
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| author | Noureddine Azzouz Bouharket Benaissa Hüseyin Budak İzzettin Demir |
| author_facet | Noureddine Azzouz Bouharket Benaissa Hüseyin Budak İzzettin Demir |
| author_sort | Noureddine Azzouz |
| collection | DOAJ |
| description | Abstract In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of ψ-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and Hölder’s integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann–Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions. |
| format | Article |
| id | doaj-art-b2eceb91ea1c4b0aa0cd0f615b7e0751 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-b2eceb91ea1c4b0aa0cd0f615b7e07512025-02-09T12:47:45ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025112310.1186/s13661-025-02001-1Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operatorsNoureddine Azzouz0Bouharket Benaissa1Hüseyin Budak2İzzettin Demir3Faculty of Sciences, University Center Nour Bachir El Bayadh DZFaculty of Material Sciences, University of TiaretDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityAbstract In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of ψ-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and Hölder’s integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann–Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions.https://doi.org/10.1186/s13661-025-02001-1h-convex functionRiemann-Liouville fractional integralsψ-Hilfer integral operatorHermite-Hadamard-Mercer inequality |
| spellingShingle | Noureddine Azzouz Bouharket Benaissa Hüseyin Budak İzzettin Demir Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators Boundary Value Problems h-convex function Riemann-Liouville fractional integrals ψ-Hilfer integral operator Hermite-Hadamard-Mercer inequality |
| title | Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators |
| title_full | Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators |
| title_fullStr | Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators |
| title_full_unstemmed | Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators |
| title_short | Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators |
| title_sort | hermite hadamard mercer type inequalities for fractional integrals a study with h convexity and ψ hilfer operators |
| topic | h-convex function Riemann-Liouville fractional integrals ψ-Hilfer integral operator Hermite-Hadamard-Mercer inequality |
| url | https://doi.org/10.1186/s13661-025-02001-1 |
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