Hermite–Hadamard-type inequalities arising from tempered fractional integrals including twice-differentiable functions
UDC 517.5 We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7640 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators. We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types. The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals. |
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| DOI: | 10.3842/umzh.v76i9.7640 |