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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-025-02001-1 |
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| Summary: | 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. |
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| ISSN: | 1687-2770 |